On the Kodaira--Saito vanishing theorem of weakly ample divisor

Yongpan Zou

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On the Kodaira--Saito vanishing theorem of weakly ample divisor

Yongpan Zou

Algebraic Geometry · Submitted 2 Aug 2023

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

The authors' main claim On smooth projective variety, for a reduced effective divisor which is weakly ample in the sense of cohomology, we introduce a Kadaira--Saito vanishing theorem for it.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,640 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.06 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

On smooth projective variety, for a reduced effective divisor which is weakly ample in the sense of cohomology, we introduce a Kadaira--Saito vanishing theorem for it.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	On smooth projective variety, for a reduced effective divisor which is weakly ample in the sense of cohomology, we introduce a Kadaira--Saito vanishing theorem for it.	contribution 0.90	0.90	0.87	asserted 1.00

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arXiv listing abstract v1

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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

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Original abstract

On smooth projective variety, for a reduced effective divisor which is weakly ample in the sense of cohomology, we introduce a Kadaira--Saito vanishing theorem for it.

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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

What it cites · 4 sentences without a confident label

Cites as background 3 papers

Recently, there are $L^2$-approaches to the Saito Vanishing Theorem, see [ref] and [ref] for details.

Vanishing theorem for tame harmonic bundles via $L^2$-cohomology · Introduction · 0.82
Recently, there are $L^2$-approaches to the Saito Vanishing Theorem, see [ref] and [ref] for details.

2306.00313 · Introduction · 0.82
[ref] Let $X$ be a complex manifold and let $D = ∑_i=1^r D_i$ be a simple normal crossing divisor on $X$.

On the nilpotent orbit theorem of complex variations of Hodge structure · Preliminaries · 0.93

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