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Paper Citation Record · LEDGER

Degree functions of graded families of ideals

As of 8 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 0 inbound Pith citation observations for arXiv:2506.05248.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.05248 v1

Coverage vector

measured 54 of 54 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:33:18.800058Z

measured 54 of 54 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

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measured 0 of 1 external citation measurements

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Reference resolution

54 of 54 outbound references displayed

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External citation measurements

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Outbound references

Observation 5aa70e63-92e1-41fd-8a58-58239578060d · outbound

This paper cites Abhyankar, On the valuations centered in a local domain, Amer.

Degree functions of graded families of ideals Abhyankar, On the valuations centered in a local domain, Amer

Reference 1

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Observation fc78bea1-742c-444e-aa01-e16e51e99f02 · outbound

This paper cites Artin, On the solutions of analytic equations, Invent.

Degree functions of graded families of ideals Artin, On the solutions of analytic equations, Invent

Reference 2

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Observation 3b88231a-b617-4fb1-bd49-0da4f84657ce · outbound

This paper cites Artin, Lipman’s proof of resolution of singularities for surfaces, pp.

Degree functions of graded families of ideals Artin, Lipman’s proof of resolution of singularities for surfaces, pp

Reference 3

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Observation 361dcb04-cfea-4845-8ced-53c1ad0d8e58 · outbound

This paper cites Barth, C.

Degree functions of graded families of ideals Barth, C

Reference 4

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Observation 0275bf49-0081-497f-8571-6ed0a5155095 · outbound

This paper cites Rational powers, invariant ideals, and the summation formula.

Degree functions of graded families of ideals Rational powers, invariant ideals, and the summation formula

Reference 5

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Observation 7f6912e0-ece6-4e01-9cee-c42d3e4b0718 · outbound

This paper cites an unresolved cited work.

Degree functions of graded families of ideals Unresolved cited work

Reference 6

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Observation d135062c-b824-4207-a110-095343b137d4 · outbound

This paper cites Bourbaki, Commutative Algebra, Chapters 1-7, Springer Verlag, 1989.

Degree functions of graded families of ideals Bourbaki, Commutative Algebra, Chapters 1-7, Springer Verlag, 1989

Reference 7

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Observation 07f67c2c-6919-451a-85d8-b7d4dfc432a6 · outbound

This paper cites Relative mixed multiplicities and mixed Buchsbaum-Rim multiplicities.

Degree functions of graded families of ideals Relative mixed multiplicities and mixed Buchsbaum-Rim multiplicities

Reference 8

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Observation 94be01cb-e9c9-4b40-aa48-2ba5f353bc24 · outbound

This paper cites Multidegrees, families, and integral dependence.

Degree functions of graded families of ideals Multidegrees, families, and integral dependence

Reference 9

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Observation e1863e9b-dbd9-4138-beee-9ccad6c276bc · outbound

This paper cites Cossart, U.

Degree functions of graded families of ideals Cossart, U

Reference 10

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Observation 1255862d-4843-4e21-8237-e3208ec78648 · outbound

This paper cites Cutkosky, On unique and almost unique factorization of complete ideals II, Inventiones Math.

Degree functions of graded families of ideals Cutkosky, On unique and almost unique factorization of complete ideals II, Inventiones Math

Reference 11

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Observation b081a2b8-3afe-45d0-892e-6aa1a956260c · outbound

This paper cites Cutkosky, Asymptotic multiplicities of graded families of ideals and linear series, Adv.

Degree functions of graded families of ideals Cutkosky, Asymptotic multiplicities of graded families of ideals and linear series, Adv

Reference 12

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Observation faf00e77-e614-4e70-9ebe-ee92295e1579 · outbound

This paper cites Cutkosky, A general volume=multiplicity formula, Acta Math.

Degree functions of graded families of ideals Cutkosky, A general volume=multiplicity formula, Acta Math

Reference 13

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Observation 840dbd5a-7c3f-43f3-81f1-3602ef0fdef3 · outbound

This paper cites Cutkosky, Mixed multiplicities of divisorial filtrations, Adv.

Degree functions of graded families of ideals Cutkosky, Mixed multiplicities of divisorial filtrations, Adv

Reference 14

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Observation d0b4880f-1c96-4785-ab01-60f39921dcb9 · outbound

This paper cites Cutkosky, Analytic Spread of filtrations on two dimensional normal local rings, Nagoya Math.

Degree functions of graded families of ideals Cutkosky, Analytic Spread of filtrations on two dimensional normal local rings, Nagoya Math

Reference 15

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Observation 225691fb-ff6f-4a1c-a918-cc3b82955c9c · outbound

This paper cites Cutkosky, Rees algebras and the reduced fiber cone of divisorial filtrations on two dimensional normal local rings, Commun.

Degree functions of graded families of ideals Cutkosky, Rees algebras and the reduced fiber cone of divisorial filtrations on two dimensional normal local rings, Commun

Reference 16

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Observation cb80766c-341d-4e39-a21e-a117c6524e8a · outbound

This paper cites The Rees algebra and analytic spread of a divisorial filtration.

Degree functions of graded families of ideals The Rees algebra and analytic spread of a divisorial filtration

Reference 17

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Observation 0203fd76-b9e0-4c9d-8197-39260a4db2b9 · outbound

This paper cites Cutkosky and P.

Degree functions of graded families of ideals Cutkosky and P

Reference 18

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Observation b5a97b16-3c6d-4ccc-8811-01f986ff6674 · outbound

This paper cites Cutkosky and H.

Degree functions of graded families of ideals Cutkosky and H

Reference 19

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Observation 4bd15f1d-6006-48ad-984f-71fd82f98991 · outbound

This paper cites Multiplicities and degree functions in local rings via intersection products.

Degree functions of graded families of ideals Multiplicities and degree functions in local rings via intersection products

Reference 20

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Observation b100cab4-d5e0-472d-b628-06d5606942cc · outbound

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Degree functions of graded families of ideals Unresolved cited work

Reference 21

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Observation e8ca2062-0e27-4294-8903-58fa371c0e27 · outbound

This paper cites Fulton, Intersection Theory, second edition, Springer, 1998.

Degree functions of graded families of ideals Fulton, Intersection Theory, second edition, Springer, 1998

Reference 22

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Observation c3aa43fb-5d5a-4840-8f03-01c848e4e890 · outbound

This paper cites Goel, R.V.

Degree functions of graded families of ideals Goel, R.V

Reference 23

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Observation 5c7848da-9853-430c-8630-a7720761a033 · outbound

This paper cites Grauert, uber modifikationen und exceptilonelle analytischen mengen, Math.

Degree functions of graded families of ideals Grauert, uber modifikationen und exceptilonelle analytischen mengen, Math

Reference 24

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Observation 94f6539b-3868-4d02-844d-39f4e217420a · outbound

This paper cites Grothendieck, Éléments de géométrie algébrique II, Étude globale élémentaire de quelques classes de morphisms, Pub.

Degree functions of graded families of ideals Grothendieck, Éléments de géométrie algébrique II, Étude globale élémentaire de quelques classes de morphisms, Pub

Reference 25

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Observation bc5a31e8-bfe4-414f-92f6-6e40d4ce7d11 · outbound

This paper cites Grothendieck, Éléments de géométrie algébrique IV , Étude locale des Schémas et des Morphismes des Schémas (Seconde Partie), Pub.

Degree functions of graded families of ideals Grothendieck, Éléments de géométrie algébrique IV , Étude locale des Schémas et des Morphismes des Schémas (Seconde Partie), Pub

Reference 26

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Observation 24e7bb6a-cdd3-4492-8aac-6f8c7f29545b · outbound

This paper cites Hartshorne, Algebraic Geometry, Springer, 1978.

Degree functions of graded families of ideals Hartshorne, Algebraic Geometry, Springer, 1978

Reference 27

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Observation 3f639e46-7799-4c4a-86be-3082b45521f6 · outbound

This paper cites Hironaka, On the equaivalence of singularities, I, Arithmetical Algebraic Geometry, Proceedings.

Degree functions of graded families of ideals Hironaka, On the equaivalence of singularities, I, Arithmetical Algebraic Geometry, Proceedings

Reference 28

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Observation d0e1f1f6-a096-47ba-83ed-6dd07fc90627 · outbound

This paper cites Katz and J.

Degree functions of graded families of ideals Katz and J

Reference 29

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Observation 07cba6b9-c87c-4338-a856-6cfb1e0e7c9f · outbound

This paper cites Kleiman, Toward a numerical theory of ampleness, Ann.

Degree functions of graded families of ideals Kleiman, Toward a numerical theory of ampleness, Ann

Reference 30

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Observation 23dcb11f-6a29-4639-8533-3a9abb680b0e · outbound

This paper cites Kleiman and A.

Degree functions of graded families of ideals Kleiman and A

Reference 31

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source=pdf_text observed=2026-08-07T10:33:18.677622Z digest=sha256:1a3f71d8e9e787b60e684353c2d547eab246ee95c701edbedb1bee8975d956f6

Observation af3109e9-bb9d-439e-b835-6a941c5698f9 · outbound

This paper cites Laufer, On deformations of resolutions of two-dimensional singularities, Rice University studies in complex analysis, 1972.

Degree functions of graded families of ideals Laufer, On deformations of resolutions of two-dimensional singularities, Rice University studies in complex analysis, 1972

Reference 32

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source=pdf_text observed=2026-08-07T10:33:18.682645Z digest=sha256:59c27084a16dd416efc8914bd49ef523424f970ff1dd16cec8c7b36d16d0e89a

Observation 53d1e50a-4afa-4d3a-abc1-be0ce3ccf323 · outbound

This paper cites Lazarsfeld, Positivity in Algebraic Geometry I, Springer, 2000.

Degree functions of graded families of ideals Lazarsfeld, Positivity in Algebraic Geometry I, Springer, 2000

Reference 33

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Observation e2cb0d6e-ac05-4f62-b841-281d56e4a687 · outbound

This paper cites Lazarsfeld and M.

Degree functions of graded families of ideals Lazarsfeld and M

Reference 34

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source=pdf_text observed=2026-08-07T10:33:18.693111Z digest=sha256:d15489cf9ed73faae63632dac99a2e37c04772dbbaecef09e055fb27cdb85e1b

Observation 6980a0ba-8ac8-4729-ac0e-43b2986f69b5 · outbound

This paper cites Lin, Algebraic Geometry and Arithmetic Curves, Oxford graduate texts in mathematics 6, translated by Reinie Erné, Oxford University Press, 2002.

Degree functions of graded families of ideals Lin, Algebraic Geometry and Arithmetic Curves, Oxford graduate texts in mathematics 6, translated by Reinie Erné, Oxford University Press, 2002

Reference 35

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raw_fallback, observed 2026-08-07T10:33:19.366999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.697995Z digest=sha256:b4067bc7583ada9e48c0831596d42e9296591879657c990c5d09ba1db6dd5bcb

Observation d3d44f1c-5ad6-4384-9817-54cf73c59d2e · outbound

This paper cites Lipman, Rational singularities with applications to algebraic surfaces and unique factorization, Publ.

Degree functions of graded families of ideals Lipman, Rational singularities with applications to algebraic surfaces and unique factorization, Publ

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.349974Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.703505Z digest=sha256:9551ee6641328b7cda85a139e5fcf71c5a98b63cbec5bf1f525168b531ba54c5

Observation 2014c4b1-1bbd-4e97-aba5-e7673c80e8e9 · outbound

This paper cites Lipman, Desingularization of 2-dimensional schemes, Annals of Math.

Degree functions of graded families of ideals Lipman, Desingularization of 2-dimensional schemes, Annals of Math

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.332894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.708402Z digest=sha256:5aed6df2a2e78ab9fbca4233e7f3a651551c7f6c1dd8c2a8b5188f22057a3ac5

Observation bd4a16fa-cedd-4e53-9f0a-530a2149b0fd · outbound

This paper cites Matsumura, Commutative Ring Theory, Cambridge studies in advanced mathematics 8, Cambridge University Press, 1989.

Degree functions of graded families of ideals Matsumura, Commutative Ring Theory, Cambridge studies in advanced mathematics 8, Cambridge University Press, 1989

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.315076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.713390Z digest=sha256:ed4ef8f302a25b498b8483b0e4f79beffbbcf7c96600569345efd260b0ac1916

Observation bd82d18c-b62a-409c-a61c-e9cec470281a · outbound

This paper cites Milne, Étale cohomology, Princeton University Press, 1980.

Degree functions of graded families of ideals Milne, Étale cohomology, Princeton University Press, 1980

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.298687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.718735Z digest=sha256:b17b42bc27406b3ccbd6b1ea71668b9978d8bd013aad35414ff7d81d59d3b472

Observation e39067c5-d8a7-4e25-ace6-1a254e18b0bc · outbound

This paper cites Mumford, Lectures on curves on an algebraic surface, Annals of Math.

Degree functions of graded families of ideals Mumford, Lectures on curves on an algebraic surface, Annals of Math

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.281058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.723859Z digest=sha256:7fe83dd8c4065657fa88b1cc2d262e2f1d6f84d9c3526c3c8f85d375682dd395

Observation edfa816f-59c9-4a3c-906a-455ff28ade06 · outbound

This paper cites Polstra, Zariski-Nagata theorem for singularities and the uniform Izumi-Rees property, preprint arXiv:2406.00759 (2024).

Degree functions of graded families of ideals Polstra, Zariski-Nagata theorem for singularities and the uniform Izumi-Rees property, preprint arXiv:2406.00759 (2024)

Reference 41

Resolution
verified exact
raw_fallback, observed 2026-08-07T10:33:18.926671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.729049Z digest=sha256:86c65930b41143b0295aea8418b04e70d0b0435ed4e50985b097364308bc76ed

Observation dcd44eb2-b972-4243-a328-885fd5dfbe67 · outbound

This paper cites Ramanujam, A geometric interpretation of multiplicity, Inventiones Math.

Degree functions of graded families of ideals Ramanujam, A geometric interpretation of multiplicity, Inventiones Math

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.263690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.734302Z digest=sha256:d99929aff5515cd5995e88c97f3ddf90ca937497838dd92e6b72683baefcf60b

Observation 1a0abb18-d68f-4852-8a76-931c43cd4e62 · outbound

This paper cites Rees, Valuations associated with ideals (II), J.

Degree functions of graded families of ideals Rees, Valuations associated with ideals (II), J

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.246422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.739381Z digest=sha256:9612ba4e79557330e307cfa88d41b2cdf08a5a33aba63506cd48a4b7f49e86c6

Observation ba3d7cef-95c5-473f-91f6-46c07e4fa86b · outbound

This paper cites Rees, A note on analytically unramified local rings, J.

Degree functions of graded families of ideals Rees, A note on analytically unramified local rings, J

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.230035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.744868Z digest=sha256:8012874a021221c925cc7d41b319a04b88cb26a8d32bb3d9ade0910ea7b1889c

Observation 5817e773-e2db-46af-adf0-f751b3d6e0f8 · outbound

This paper cites Rees, Degree functions in local rings, Proceedings of the Cambridge Phil.

Degree functions of graded families of ideals Rees, Degree functions in local rings, Proceedings of the Cambridge Phil

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.213209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.750919Z digest=sha256:fab9ab279626aaae77ae0e4abe3c2605d1d5ddcbf5203bcc14cb110ed40b0c62

Observation 76995c9a-b948-4520-9834-91c5e3e80f2f · outbound

This paper cites Rees and Y.

Degree functions of graded families of ideals Rees and Y

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.196793Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.756382Z digest=sha256:c9d74eb7c625a0d31a192fdedabeeb64df06d270989f36b635a32921712f3fb3

Observation 15dd47d3-af21-43db-b14b-be3ec5eb9935 · outbound

This paper cites Rees, Lectures on the asymptotic theory of ideals, London Math Soc.

Degree functions of graded families of ideals Rees, Lectures on the asymptotic theory of ideals, London Math Soc

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.181145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.762105Z digest=sha256:1211ba076116b12696b2dfd69c286385a144a3c9191d9c0f9625a78817bfae96

Observation 3dd0d198-5f24-4ab5-98a2-c0b5c8f4214d · outbound

This paper cites Samuel, Sur les variétés algébroides, Ann.

Degree functions of graded families of ideals Samuel, Sur les variétés algébroides, Ann

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.163251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.766921Z digest=sha256:3623fcb03141f64d261635f00ff2bf034b924fd1656f3bd79418dd27f9be0c10

Observation 2894f9ac-41bb-4cf1-a3cc-c23f644f6c21 · outbound

This paper cites Snapper, Polynomials associated with divisors, J.

Degree functions of graded families of ideals Snapper, Polynomials associated with divisors, J

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.145178Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.772465Z digest=sha256:2a0fe093e3e7a73a4046cf2618729ee281f297926ffc4f10d36cf6ef0239a867

Observation e53499a7-3c23-4598-b9c4-fed9cd845cf4 · outbound

This paper cites The stacks project.

Degree functions of graded families of ideals The stacks project

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.125854Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.777604Z digest=sha256:e3cf769aa01baf64e9dafd0a85f50cb79ee23e65b1c9fc458efb549332561d64

Observation 80a40305-8aa4-41d6-9a67-19f3505a4109 · outbound

This paper cites Swanson and C.

Degree functions of graded families of ideals Swanson and C

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.109430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.782785Z digest=sha256:0c5d2d7062541ea8ff2bc23f925589653840aa7194249d97a16010574819ddbd

Observation d1ab4ec0-5310-4590-8988-341187187732 · outbound

This paper cites Thorup, Rational equivalence theory on arbitrary Noetherian schemes, In Enumerative Geometry, Sebastian Xambó-Descamps Ed, LNM 1436, Springer, 1990.

Degree functions of graded families of ideals Thorup, Rational equivalence theory on arbitrary Noetherian schemes, In Enumerative Geometry, Sebastian Xambó-Descamps Ed, LNM 1436, Springer, 1990

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.075588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.794685Z digest=sha256:b686c10c7541612048c3aa74534a570c9041fd814674536e82de73538786ac59

Observation 157aa161-825e-483e-bd84-7b80a1a00cfc · outbound

This paper cites Zariski and P.

Degree functions of graded families of ideals Zariski and P

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.056995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.800058Z digest=sha256:435496d8f8ee78f4daa95179911ce2f9f5813727500560c9037c2eaea449510d

Observation 9c7fb9e4-c8c7-4227-a2c7-e19ed3949e42 · outbound

This paper cites an unresolved cited work.

Degree functions of graded families of ideals Unresolved cited work

Reference 336

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:33:19.093193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T10:33:18.789156Z digest=sha256:e21f104cf36e2a413a0662aacddd3d1681d0650490bb6e3c219f595cb4792149

Pith citing papers

No inbound Pith citation observations are available.