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Differential zeros of period integrals and generalized hypergeometric functions

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Jingyue Chen, An Huang, Bong H. Lian, Shing-Tung Yau

Algebraic Geometry · Submitted 3 Sep 2017

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

The authors' main claim As applications, we prove that the locus is algebraic and in some cases, non-empty.

how it is stated · asserted 0.98 read the record →

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arXiv ID1709.00713 (version 4)
Pith IDDCXNDUVH, Pith's permanent record of this paper and its review
CitationAn Huang, Bong H. Lian, Jingyue Chen, Shing-Tung Yau. "Differential zeros of period integrals and generalized hypergeometric functions." arXiv:1709.00713 (2017). https://pith.science/paper/DCXNDUVH
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,275 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.55 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.23 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

In this paper, we study the zero loci of local systems of the form $\delta\Pi$, where $\Pi$ is the period sheaf of the universal family of CY hypersurfaces in a suitable ambient space $X$, and $\delta$ is a given differential operator on the space of sections $V^\vee=\Gamma(X,K_X^{-1})$. Using earlier results of three of the authors and their collaborators, we give several different descriptions of the zero locus of $\delta\Pi$. As applications, we prove that the locus is algebraic and in some cases, non-empty. We also give an explicit way to compute the polynomial defining equations of the locus in some cases. This description gives rise to a natural stratification to the zero locus.

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 In this paper, we study the zero loci of local systems of the form $\delta\Pi$, where $\Pi$ is the period sheaf of the universal family of CY hypersurfaces in a suitable ambient space $X$, and $\delta$ is a given differential operator on the space of sections $V^\vee=\Gamma(X,K_X^{-1})$. contribution 0.90 0.49 0.06 asserted 0.88
s1 Using earlier results of three of the authors and their collaborators, we give several different descriptions of the zero locus of $\delta\Pi$. contribution 0.60 0.84 0.07 asserted 1.00
s2 As applications, we prove that the locus is algebraic and in some cases, non-empty. result 0.99 0.94 0.43 asserted 0.98
s3 We also give an explicit way to compute the polynomial defining equations of the locus in some cases. contribution 0.60 0.94 0.11 asserted 0.97
s4 This description gives rise to a natural stratification to the zero locus. result 0.65 0.86 0.10 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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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

In this paper, we study the zero loci of local systems of the form $\delta\Pi$, where $\Pi$ is the period sheaf of the universal family of CY hypersurfaces in a suitable ambient space $X$, and $\delta$ is a given differential operator on the space of sections $V^\vee=\Gamma(X,K_X^{-1})$. Using earlier results of three of the authors and their collaborators, we give several different descriptions of the zero locus of $\delta\Pi$. As applications, we prove that the locus is algebraic and in some cases, non-empty. We also give an explicit way to compute the polynomial defining equations of the locus in some cases. This description gives rise to a natural stratification to the zero locus.

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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

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