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Invariance of plurigenera and good minimal models

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Iacopo Brivio

Algebraic Geometry · Submitted 17 Jul 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We generalize his result to families of singular pairs over DVRs of positive or mixed characteristic.

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arXiv ID2207.08107 (version 2)
Pith IDJEB4N5UP, Pith's permanent record of this paper and its review
CitationIacopo Brivio. "Invariance of plurigenera and good minimal models." arXiv:2207.08107 (2022). https://pith.science/paper/JEB4N5UP
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,000 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.37 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.49 · compares with prior results 0.88 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Nakayama showed that deformation invariance of plurigenera for smooth complex varieties follows from the MMP and Abundance Conjectures. We generalize his result to families of singular pairs over DVRs of positive or mixed characteristic. As an application we show invariance of plurigenera for deformations of good minimal models of general type varieties whose canonical model has rational singularities as well as boundedness of Gorenstein canonical models of dimension three and fixed volume over an algebraically closed field of characteristic $p>5$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Nakayama showed that deformation invariance of plurigenera for smooth complex varieties follows from the MMP and Abundance Conjectures. background 1.00 0.02 0.05 asserted 1.00
s1 We generalize his result to families of singular pairs over DVRs of positive or mixed characteristic. contribution 0.99 0.93 0.26 asserted 0.99
s2 As an application we show invariance of plurigenera for deformations of good minimal models of general type varieties whose canonical model has rational singularities as well as boundedness of Gorenstein canonical models of dimension three and fixed volume over an algebraically closed field of characteristic $p>5$. result 0.88 0.94 0.64 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Nakayama showed that deformation invariance of plurigenera for smooth complex varieties follows from the MMP and Abundance Conjectures. We generalize his result to families of singular pairs over DVRs of positive or mixed characteristic. As an application we show invariance of plurigenera for deformations of good minimal models of general type varieties whose canonical model has rational singularities as well as boundedness of Gorenstein canonical models of dimension three and fixed volume over an algebraically closed field of characteristic $p>5$.

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References
How the literature uses it

2 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 4 sentences without a confident label

Uses its method or tool 1 paper
  • By "spreading out techniques" (see for example [ref] and [ref] ), there exist $U ⊆Z$ dense open subset and a finite map $φU' →U$ such that, if $Y_U'$ is the normalisation of the main component of $f^-1(U) ×_U U'$, there exists a birational map $σY_U →Y_U'$ with $Y_U, η̅= Y̅$.

    On the canonical bundle formula in positive characteristic · Discriminant and moduli parts · 0.95

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