The volume function is upper semicontinuous on families of divisors | Paper Citation Record

Observation 4da11470-abff-4f1a-89cc-2fd69ae5ccc2 · outbound

This paper cites Abramovich and K.

The volume function is upper semicontinuous on families of divisors Abramovich and K

Reference 1

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Observation db9e6a3f-440b-49e6-ad9c-3363d0fda51d · outbound

This paper cites Alexeev, C.

The volume function is upper semicontinuous on families of divisors Alexeev, C

Reference 2

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Observation 46aa4501-052a-4ec2-84fb-19c228732333 · outbound

This paper cites Ambro, Quasi-log varieties, Tr.

The volume function is upper semicontinuous on families of divisors Ambro, Quasi-log varieties, Tr

Reference 3

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Observation a3e8793a-48f1-4d56-bec7-d2896c28ac29 · outbound

This paper cites Ambro, The moduli b-divisor of an lc-trivial fibration, Compos.

The volume function is upper semicontinuous on families of divisors Ambro, The moduli b-divisor of an lc-trivial fibration, Compos

Reference 4

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Observation 416d51cb-da57-4849-99cc-56c915c851e7 · outbound

This paper cites Birkar, Ascending chain condition for log canonical thresholds and termination of log flips, Duke Math.

The volume function is upper semicontinuous on families of divisors Birkar, Ascending chain condition for log canonical thresholds and termination of log flips, Duke Math

Reference 5

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Observation 34a0e493-2d09-4ce1-bad8-435de7cd8308 · outbound

This paper cites Birkar, Existence of log canonical flips and a special LMMP, Pub.

The volume function is upper semicontinuous on families of divisors Birkar, Existence of log canonical flips and a special LMMP, Pub

Reference 6

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Observation 88da95ee-caff-4ee7-a9b8-d02c7e78528d · outbound

This paper cites Birkar, On existence of log minimal models and weak Zariski decompositions, Math.

The volume function is upper semicontinuous on families of divisors Birkar, On existence of log minimal models and weak Zariski decompositions, Math

Reference 7

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Observation 3a504091-87c6-4c46-9479-fbb7303d6953 · outbound

This paper cites Birkar, Anti-pluricanonical systems on Fano varieties.

The volume function is upper semicontinuous on families of divisors Birkar, Anti-pluricanonical systems on Fano varieties

Reference 8

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Observation 6de10459-9024-436d-98e3-f0a47ce4a4d5 · outbound

This paper cites Generalised pairs in birational geometry.

The volume function is upper semicontinuous on families of divisors Generalised pairs in birational geometry

Reference 9

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Observation ff55bcf8-b578-4b7d-af9a-1082ac1d38c4 · outbound

This paper cites On connectedness of non-klt loci of singularities of pairs.

The volume function is upper semicontinuous on families of divisors On connectedness of non-klt loci of singularities of pairs

Reference 10

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Observation 3945baaa-bc24-4bab-99dd-d65bfb0884cf · outbound

This paper cites Birkar, Singularities of linear systems and boundedness of Fano varieties, Ann.

The volume function is upper semicontinuous on families of divisors Birkar, Singularities of linear systems and boundedness of Fano varieties, Ann

Reference 11

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Observation e923978d-7f5b-4e1b-853c-bcfbb72a8f7a · outbound

This paper cites Boundedness and volume of generalised pairs.

The volume function is upper semicontinuous on families of divisors Boundedness and volume of generalised pairs

Reference 12

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Observation b5ca0b81-ea2a-4552-bf68-6296e2e88b8c · outbound

This paper cites Birkar, Geometry of polarised varieties, Pub.

The volume function is upper semicontinuous on families of divisors Birkar, Geometry of polarised varieties, Pub

Reference 13

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Observation 32e44e36-7ccd-4e8b-b6bb-85e43a8439ca · outbound

This paper cites Birkar, Singularities on Fano fibrations and beyond, arXiv: 2305.18770v1.

The volume function is upper semicontinuous on families of divisors Birkar, Singularities on Fano fibrations and beyond, arXiv: 2305.18770v1

Reference 14

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Observation e55ba2c1-8e87-4101-ae9d-da514b8cf343 · outbound

This paper cites Birkar, Boundedness of Fano type fibrations, Ann.

The volume function is upper semicontinuous on families of divisors Birkar, Boundedness of Fano type fibrations, Ann

Reference 15

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Observation d8fcdb7d-5e79-4381-b20b-804986b5f3c6 · outbound

This paper cites Birkar, P.

The volume function is upper semicontinuous on families of divisors Birkar, P

Reference 16

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Observation aebec131-8ff5-4f21-aaa5-b79d5f10be37 · outbound

This paper cites Boundedness of elliptic Calabi-Yau varieties with a rational section.

The volume function is upper semicontinuous on families of divisors Boundedness of elliptic Calabi-Yau varieties with a rational section

Reference 17

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Observation 53df33e7-f830-4d39-8e7e-0f4c48db12aa · outbound

This paper cites Birkar and Z.

The volume function is upper semicontinuous on families of divisors Birkar and Z

Reference 18

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Observation c8cc1f0e-28b5-4558-9a18-607f097e7f8d · outbound

This paper cites an unresolved cited work.

The volume function is upper semicontinuous on families of divisors Unresolved cited work

Reference 19

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Observation eb807d89-349d-40e8-bc9c-5a13f379db78 · outbound

This paper cites Birkar and D.-Q.

The volume function is upper semicontinuous on families of divisors Birkar and D.-Q

Reference 20

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Observation 3bd5b122-ce2e-4df5-ae1a-281db047824a · outbound

This paper cites Math, 378 (2021), 107541.

The volume function is upper semicontinuous on families of divisors Math, 378 (2021), 107541

Reference 21

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Observation 08f39424-2b04-4a49-a83b-c2d22a0349d6 · outbound

This paper cites Boundedness of $n$-complements for generalized pairs.

The volume function is upper semicontinuous on families of divisors Boundedness of $n$-complements for generalized pairs

Reference 22

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Observation d3539bb3-7de8-4841-9638-54c19dee1276 · outbound

This paper cites On generalized minimal log discrepancy.

The volume function is upper semicontinuous on families of divisors On generalized minimal log discrepancy

Reference 23

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Observation c3f4af7c-f2c9-4ff7-b0a8-d18d9b76c53c · outbound

This paper cites Chen and J.

The volume function is upper semicontinuous on families of divisors Chen and J

Reference 24

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Observation 9380649d-db9e-4b21-b6af-6cc9da168d14 · outbound

This paper cites an unresolved cited work.

The volume function is upper semicontinuous on families of divisors Unresolved cited work

Reference 25

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Observation 1573c483-6153-4344-b77d-6d14ff491398 · outbound

This paper cites On the termination of flips for log canonical generalized pairs.

The volume function is upper semicontinuous on families of divisors On the termination of flips for log canonical generalized pairs

Reference 26

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Observation deade073-359a-41e1-a229-bb9137da208c · outbound

This paper cites Chen and Q.

The volume function is upper semicontinuous on families of divisors Chen and Q

Reference 27

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Observation c2cc8ab1-fd7b-43c5-9a6c-9e6e9d4000a3 · outbound

This paper cites Choi, The geography of log models and its applications, PhD Thesis, Johns Hopkins University (2008).

The volume function is upper semicontinuous on families of divisors Choi, The geography of log models and its applications, PhD Thesis, Johns Hopkins University (2008)

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.474245Z

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Observation d5237690-6830-48cd-bdff-6e3930214226 · outbound

This paper cites Filipazzi, Boundedness of Log Canonical Surface Generalized Polarized Pairs, Taiwanese J.

The volume function is upper semicontinuous on families of divisors Filipazzi, Boundedness of Log Canonical Surface Generalized Polarized Pairs, Taiwanese J

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Observation a06d176c-5186-4c4d-8614-2a1767dec1a0 · outbound

This paper cites On a generalized canonical bundle formula and generalized adjunction.

The volume function is upper semicontinuous on families of divisors On a generalized canonical bundle formula and generalized adjunction

Reference 30

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Observation a96cd53e-40e8-425a-9a6b-5e243c11eda3 · outbound

This paper cites Restricted volumes and base loci of linear series.

The volume function is upper semicontinuous on families of divisors Restricted volumes and base loci of linear series

Reference 31

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Observation cad168d1-e9ef-4d97-94bb-799ea9b6a689 · outbound

This paper cites On the boundedness of $n$-folds with $\kappa(X)=n-1$.

The volume function is upper semicontinuous on families of divisors On the boundedness of $n$-folds with $\kappa(X)=n-1$

Reference 32

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Observation c6a7c6d3-f14e-4a92-8860-9fc894f09cff · outbound

This paper cites Invariance of Plurigenera and boundedness for Generalized Pairs.

The volume function is upper semicontinuous on families of divisors Invariance of Plurigenera and boundedness for Generalized Pairs

Reference 33

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Observation 8e54857a-d330-48f1-a74d-3f8a6664a0f1 · outbound

This paper cites On the connectedness principle and dual complexes for generalized pairs.

The volume function is upper semicontinuous on families of divisors On the connectedness principle and dual complexes for generalized pairs

Reference 34

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Observation beae5bbf-33a4-4860-90c0-09f9e7eee8a8 · outbound

This paper cites Connectedness principle for $3$-folds in characteristic $p>5$.

The volume function is upper semicontinuous on families of divisors Connectedness principle for $3$-folds in characteristic $p>5$

Reference 35

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Observation 058dabdc-d675-4de5-a4ca-d050dc0bc6a3 · outbound

This paper cites Fujita, Approximating Zariski decomposition of big line bundles, Kodai Math.

The volume function is upper semicontinuous on families of divisors Fujita, Approximating Zariski decomposition of big line bundles, Kodai Math

Reference 36

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Observation 18b5d107-34b1-468b-b127-cd916bf651cd · outbound

This paper cites Fujino, Termination of 4 -fold canonical flips, Publ.

The volume function is upper semicontinuous on families of divisors Fujino, Termination of 4 -fold canonical flips, Publ

Reference 37

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Observation 7d8df1c3-1364-48a7-9148-fff1f4eef8e4 · outbound

This paper cites Termination of 4 -fold canonical flips.

The volume function is upper semicontinuous on families of divisors Termination of 4 -fold canonical flips

Reference 38

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Observation 29d69e2f-a345-4894-9083-96f72cc70ea6 · outbound

This paper cites Fujino, On Kawamata’s theorem, Classification of Algebraic Varieties, EMS Ser.

The volume function is upper semicontinuous on families of divisors Fujino, On Kawamata’s theorem, Classification of Algebraic Varieties, EMS Ser

Reference 39

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Observation 0427305e-efa3-488c-a1b6-f1db9f40653d · outbound

This paper cites Fujino, Foundations of the minimal model program, MSJ Memoirs, 35.

The volume function is upper semicontinuous on families of divisors Fujino, Foundations of the minimal model program, MSJ Memoirs, 35

Reference 40

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Observation 5f3f00d0-d6d9-4aee-b7a6-ac44fa90535f · outbound

This paper cites Fujino, Base point free theorems: saturation, B-divisors, and canonical bundle formula, Algebra Number Theory 6 (2012), no.

The volume function is upper semicontinuous on families of divisors Fujino, Base point free theorems: saturation, B-divisors, and canonical bundle formula, Algebra Number Theory 6 (2012), no

Reference 41

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Observation ac1a175a-a343-4bba-84ad-6d7056f1d63d · outbound

This paper cites Fujino, A transcendental approach to Koll\'ar’s injectivity theorem II, J.

The volume function is upper semicontinuous on families of divisors Fujino, A transcendental approach to Koll\'ar’s injectivity theorem II, J

Reference 42

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Observation d892ea1f-21fb-43ce-a7f5-3c2c8ba6255d · outbound

This paper cites Fundamental properties of basic slc-trivial fibrations.

The volume function is upper semicontinuous on families of divisors Fundamental properties of basic slc-trivial fibrations

Reference 43

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Observation 89b0bbca-e220-4b0b-a392-ad08b472d9de · outbound

This paper cites Corrigendum: On subadditivity of the logarithmic Kodaira dimension.

The volume function is upper semicontinuous on families of divisors Corrigendum: On subadditivity of the logarithmic Kodaira dimension

Reference 44

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Observation a120437f-ba67-4b24-941e-50379b3db263 · outbound

This paper cites Cone theorem and Mori hyperbolicity.

The volume function is upper semicontinuous on families of divisors Cone theorem and Mori hyperbolicity

Reference 45

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Observation 58fc7e2b-8484-43e9-bbaa-43d6d1fbc7e5 · outbound

This paper cites Fujino and Y.

The volume function is upper semicontinuous on families of divisors Fujino and Y

Reference 46

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Observation fc7bcdc0-49c7-4856-8356-f443f719c94c · outbound

This paper cites Existence of log canonical modifications and its applications.

The volume function is upper semicontinuous on families of divisors Existence of log canonical modifications and its applications

Reference 47

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Observation 0473e4a2-de9a-4e1d-bf21-68e11b6b4e2b · outbound

This paper cites Fulger, J.

The volume function is upper semicontinuous on families of divisors Fulger, J

Reference 48

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Observation 0a09ecd7-bf50-4826-bf14-4fdd02e6e18a · outbound

This paper cites Fujino and S.

The volume function is upper semicontinuous on families of divisors Fujino and S

Reference 49

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Observation c17f69b6-a004-4f40-abec-13a7306792e7 · outbound

This paper cites Log canonical $3$-fold complements.

The volume function is upper semicontinuous on families of divisors Log canonical $3$-fold complements

Reference 50

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Observation 1c7cfb31-1ebd-4e7a-8af1-70b5cf3daf36 · outbound

This paper cites Fukuda, On base point free theorem, Kodai Math.

The volume function is upper semicontinuous on families of divisors Fukuda, On base point free theorem, Kodai Math

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Observation ef05c415-9bf8-4d90-be36-d96d1334b334 · outbound

This paper cites Gongyo, On the minimal model theory for dlt pairs of numerical Kodaira dimension zero, Math.

The volume function is upper semicontinuous on families of divisors Gongyo, On the minimal model theory for dlt pairs of numerical Kodaira dimension zero, Math

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Observation 459d599d-424f-430a-b92d-b75b87fe2e7b · outbound

This paper cites Grothendieck, \'El\'ements de g\'eom\'etrie alg\'ebrique : IV.

The volume function is upper semicontinuous on families of divisors Grothendieck, \'El\'ements de g\'eom\'etrie alg\'ebrique : IV

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Observation 4e736ef1-5595-43f5-a7a2-4120a8cd7975 · outbound

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The volume function is upper semicontinuous on families of divisors Unresolved cited work

Reference 54

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Observation 91de3070-7418-4bd7-ad86-6a5149b3d605 · outbound

This paper cites Existence of flips for generalized lc pairs.

The volume function is upper semicontinuous on families of divisors Existence of flips for generalized lc pairs

Reference 55

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Observation 7a8144be-ea80-4b73-8855-ab23a66b43a8 · outbound

This paper cites ACC for minimal log discrepancies of terminal threefolds.

The volume function is upper semicontinuous on families of divisors ACC for minimal log discrepancies of terminal threefolds

Reference 56

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Observation b0d08db0-2ac8-4a53-ac26-f3a5a05846d1 · outbound

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The volume function is upper semicontinuous on families of divisors Unresolved cited work

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The volume function is upper semicontinuous on families of divisors Unresolved cited work

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The volume function is upper semicontinuous on families of divisors Unresolved cited work

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Observation 47f2bd28-13d5-4f30-8c6e-a2bf7377b882 · outbound

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The volume function is upper semicontinuous on families of divisors Unresolved cited work

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The volume function is upper semicontinuous on families of divisors Unresolved cited work

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Observation 73326615-e52f-42d6-899f-5903c6ce7b83 · outbound

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The volume function is upper semicontinuous on families of divisors Unresolved cited work

Reference 62

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The volume function is upper semicontinuous on families of divisors Unresolved cited work

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.638596Z

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Observation bc291b42-d3ff-4380-890a-44b2adac2ec0 · outbound

This paper cites an unresolved cited work.

The volume function is upper semicontinuous on families of divisors Unresolved cited work

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.642723Z

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Observation db1cbdeb-953b-445e-86e1-10299aabd555 · outbound

This paper cites Weak Zariski decompositions and log terminal models for generalized polarized pairs.

The volume function is upper semicontinuous on families of divisors Weak Zariski decompositions and log terminal models for generalized polarized pairs

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.646947Z

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Observation b1b8cd71-b87c-49f9-adea-a12e319ba877 · outbound

This paper cites Han and Z.

The volume function is upper semicontinuous on families of divisors Han and Z

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.651640Z

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Observation a340adba-7fbe-4a70-9142-11594222279b · outbound

This paper cites Han and Z.

The volume function is upper semicontinuous on families of divisors Han and Z

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.656133Z

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Observation bccb7937-34fd-4386-87a0-7356294b00b8 · outbound

This paper cites Effective birationality for sub-pairs with real coefficients.

The volume function is upper semicontinuous on families of divisors Effective birationality for sub-pairs with real coefficients

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.660455Z

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Observation 450d303e-21a0-40d3-8952-d67a3c6bc3c2 · outbound

This paper cites On a generalized canonical bundle formula for generically finite morphisms.

The volume function is upper semicontinuous on families of divisors On a generalized canonical bundle formula for generically finite morphisms

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.670605Z

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Observation ec4cdb77-74a1-44ba-b78d-34455549f593 · outbound

This paper cites Han and W.

The volume function is upper semicontinuous on families of divisors Han and W

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.675213Z

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Observation ab346682-2f6c-4a8e-abee-616047fb465e · outbound

This paper cites Hartshorne, Algebraic Geometry, Springer New York, NY.(1977).

The volume function is upper semicontinuous on families of divisors Hartshorne, Algebraic Geometry, Springer New York, NY.(1977)

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.679442Z

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Observation 527b6ee7-53de-43fa-b85f-d58813ca3caa · outbound

This paper cites Hashizume, Minimal model theory for relatively trivial log canonical pairs, Ann.

The volume function is upper semicontinuous on families of divisors Hashizume, Minimal model theory for relatively trivial log canonical pairs, Ann

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.684106Z

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Observation ec696bf5-39d0-4c24-9d84-a2f15056f6a6 · outbound

This paper cites Hashizume, Remarks on special kinds of the relative log minimal model program, Manuscripta Math.

The volume function is upper semicontinuous on families of divisors Hashizume, Remarks on special kinds of the relative log minimal model program, Manuscripta Math

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.689366Z

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Observation 154681ab-3f25-4159-9d2b-e5ecb3d05074 · outbound

This paper cites Finiteness of log abundant log canonical pairs in log minimal model program with scaling.

The volume function is upper semicontinuous on families of divisors Finiteness of log abundant log canonical pairs in log minimal model program with scaling

Reference 75

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.693852Z

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Observation f8f3e27a-70dc-4732-be3d-2b620b408e2f · outbound

This paper cites Non-vanishing theorem for generalized log canonical pairs with a polarization.

The volume function is upper semicontinuous on families of divisors Non-vanishing theorem for generalized log canonical pairs with a polarization

Reference 76

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.698373Z

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Observation 8726e0b6-e49e-4432-a0b0-83343ef6cc3f · outbound

This paper cites Hashizume and Z.

The volume function is upper semicontinuous on families of divisors Hashizume and Z

Reference 77

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.703766Z

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Observation 4cac6524-517f-43b7-b056-9e0b04dce754 · outbound

This paper cites ACC for minimal log discrepancies of exceptional singularities.

The volume function is upper semicontinuous on families of divisors ACC for minimal log discrepancies of exceptional singularities

Reference 78

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.708261Z

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Observation 48e5274d-52d5-443b-8e76-dc342aa71de3 · outbound

This paper cites Log abundance of the moduli b-divisors of lc-trivial fibrations.

The volume function is upper semicontinuous on families of divisors Log abundance of the moduli b-divisors of lc-trivial fibrations

Reference 79

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.712564Z

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Observation 7ce2dc13-d592-4783-ac80-b2fef5b7aa28 · outbound

This paper cites An abundance theorem for generalised pairs.

The volume function is upper semicontinuous on families of divisors An abundance theorem for generalised pairs

Reference 80

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.717360Z

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Observation f234860f-3188-4465-8227-aa2b982416ce · outbound

This paper cites Ishii, Introduction to Singularities, 2nd ed, Springer Japan KK, part of Springer Nature (2018).

The volume function is upper semicontinuous on families of divisors Ishii, Introduction to Singularities, 2nd ed, Springer Japan KK, part of Springer Nature (2018)

Reference 81

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.721934Z

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Observation c77a3d4d-e560-46e3-b7c3-b2d9bfc2620b · outbound

This paper cites Algebraic Geom.

The volume function is upper semicontinuous on families of divisors Algebraic Geom

Reference 82

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.726394Z

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Observation 3fd9d57a-291a-4152-81fa-dd8548ef12c0 · outbound

This paper cites Jiao, On the boundedness of canonical models, arXiv: 2103.13609v1.

The volume function is upper semicontinuous on families of divisors Jiao, On the boundedness of canonical models, arXiv: 2103.13609v1

Reference 83

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.730837Z

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Observation b2230a18-3e19-4029-8e80-0b67dd32db53 · outbound

This paper cites 2, 545-567.

The volume function is upper semicontinuous on families of divisors 2, 545-567

Reference 84

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.735270Z

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Observation 9da36010-f118-4771-9bbd-c697a65a616b · outbound

This paper cites Jiang, J.

The volume function is upper semicontinuous on families of divisors Jiang, J

Reference 85

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.739588Z

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Observation d4ffd4a3-5c67-4fa9-a01c-f365354e02c0 · outbound

This paper cites Kawamata, The cone of curves of algebraic varieties, Ann.

The volume function is upper semicontinuous on families of divisors Kawamata, The cone of curves of algebraic varieties, Ann

Reference 86

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.743971Z

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Observation e61c0290-cc48-4dc0-b6b5-2aff42c16ed3 · outbound

This paper cites Kawamata, On the plurigenera of minimal algebraic 3-folds with K 0 , Math.

The volume function is upper semicontinuous on families of divisors Kawamata, On the plurigenera of minimal algebraic 3-folds with K 0 , Math

Reference 87

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.748580Z

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Observation 3b85ed21-66ca-479d-82cd-50f26d0b9e3e · outbound

This paper cites Kawamata, Termination of log flips for algebraic 3 -folds, Internat.

The volume function is upper semicontinuous on families of divisors Kawamata, Termination of log flips for algebraic 3 -folds, Internat

Reference 88

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.752707Z

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Observation e8ad6066-b87d-495a-9604-0f0269f9a679 · outbound

This paper cites Kawamata, Subadjunction of log canonical divisors, II, Amer.

The volume function is upper semicontinuous on families of divisors Kawamata, Subadjunction of log canonical divisors, II, Amer

Reference 89

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.757030Z

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Observation 4bf2d51a-7480-4a0d-b43d-101275cccec5 · outbound

This paper cites Kawamata, Variation of mixed Hodge structures and the positivity for algebraic fiber spaces, Advanced Studies in Pure Mathematics, 65 (2015), 27--57.

The volume function is upper semicontinuous on families of divisors Kawamata, Variation of mixed Hodge structures and the positivity for algebraic fiber spaces, Advanced Studies in Pure Mathematics, 65 (2015), 27--57

Reference 90

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:16:06.179772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 95c3a8d7-7619-4f5d-96b4-f4cc28b38c86 · outbound

This paper cites Kawamata, K.

The volume function is upper semicontinuous on families of divisors Kawamata, K

Reference 91

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:16:06.165518Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation cbdd0636-9922-4194-bbf7-071b6ba0ad70 · outbound

This paper cites Koll\'ar, The cone theorem, Ann.

The volume function is upper semicontinuous on families of divisors Koll\'ar, The cone theorem, Ann

Reference 92

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.770236Z

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Observation 366afa30-70f3-4589-ba7a-dde198cbb549 · outbound

This paper cites Koll\'ar, Rational Curves on Algebraic Varieties.

The volume function is upper semicontinuous on families of divisors Koll\'ar, Rational Curves on Algebraic Varieties

Reference 93

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.775404Z

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Observation 70a52a43-c033-4cc1-950e-e1d40ae7d736 · outbound

This paper cites Koll\'ar, “Kodaira’s canonical bundle formula and adjunction.

The volume function is upper semicontinuous on families of divisors Koll\'ar, “Kodaira’s canonical bundle formula and adjunction

Reference 94

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.780187Z

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Observation 5590b10f-829a-460d-9f80-3bd99e50cb44 · outbound

This paper cites Koll\' a r, Singularities of the minimal model program, Cambridge Tracts in Math.

The volume function is upper semicontinuous on families of divisors Koll\' a r, Singularities of the minimal model program, Cambridge Tracts in Math

Reference 95

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.785308Z

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Observation a372493f-0553-4170-b1ae-2aa2ee4e1e34 · outbound

This paper cites Koll\' a r, Families of Varieties of General Type, Cambridge Univ.

The volume function is upper semicontinuous on families of divisors Koll\' a r, Families of Varieties of General Type, Cambridge Univ

Reference 96

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.789771Z

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Observation 10c18e39-8864-4bde-891c-c533a036ce7a · outbound

This paper cites Koll\'ar, Semi-Normal Log Centres and Deformations of Pairs, Proc.

The volume function is upper semicontinuous on families of divisors Koll\'ar, Semi-Normal Log Centres and Deformations of Pairs, Proc

Reference 97

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.794411Z

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Observation 8b3b8f3d-e93b-4ce2-bfed-26e38e70d98c · outbound

This paper cites Kempf , F.

The volume function is upper semicontinuous on families of divisors Kempf , F

Reference 98

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.799500Z

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Observation e549f44b-6625-4f96-bf37-991bbdfa5d07 · outbound

This paper cites Koll\' a r and S.

The volume function is upper semicontinuous on families of divisors Koll\' a r and S

Reference 99

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.803629Z

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Observation e719bcb4-4b4c-423d-af77-7aff6688097e · outbound

This paper cites Koll\' a r and S.

The volume function is upper semicontinuous on families of divisors Koll\' a r and S

Reference 100

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.808166Z

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Observation 6d5794b8-c24d-4a0c-bde4-36acf9a44010 · outbound

This paper cites an unresolved cited work.

The volume function is upper semicontinuous on families of divisors Unresolved cited work

Reference 101

Resolution: unresolved; no resolver link, observed 2026-08-16T11:16:04.812380Z

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