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Quantum Lefschetz theorem revisited

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Jun Wang

Algebraic Geometry · Submitted 8 May 2023

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

The authors' main claim This confirms a prediction from Coates-Corti-Iritani-Tseng about the genus zero quantum Lefschetz theorem beyond convexity.

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arXiv ID2305.04906 (version 3)
Pith ID7KL7XVZZ, Pith's permanent record of this paper and its review
CitationJun Wang. "Quantum Lefschetz theorem revisited." arXiv:2305.04906 (2023). https://pith.science/paper/7KL7XVZZ
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,318 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.73 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; .

Let $X$ be any smooth Deligne-Mumford stack with projective coarse moduli, and $Y$ be a smooth complete intersection in $X$ associated with a direct sum of semi-positive line bundles. We will introduce a useful and broad class known as admissible series for discussing quantum Lefschetz theorem. For any admissible series on the Givental's Lagrangian cone of $X$, we will show that a hypergeometric modification of the series lies on the Lagrangian cone of $Y$. This confirms a prediction from Coates-Corti-Iritani-Tseng about the genus zero quantum Lefschetz theorem beyond convexity. In our quantum Lefschetz theorem, we use extended variables to formulate the hypergeometric modification, which may be of self-independent interest.

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 Let $X$ be any smooth Deligne-Mumford stack with projective coarse moduli, and $Y$ be a smooth complete intersection in $X$ associated with a direct sum of semi-positive line bundles. background 0.99 0.10 0.02 asserted 0.66
s1 We will introduce a useful and broad class known as admissible series for discussing quantum Lefschetz theorem. contribution 0.89 0.86 0.05 asserted 0.97
s2 For any admissible series on the Givental's Lagrangian cone of $X$, we will show that a hypergeometric modification of the series lies on the Lagrangian cone of $Y$. result 0.91 0.94 0.72 asserted 1.00
s3 This confirms a prediction from Coates-Corti-Iritani-Tseng about the genus zero quantum Lefschetz theorem beyond convexity. interpretation 0.84 0.63 0.67 asserted 1.00
s4 In our quantum Lefschetz theorem, we use extended variables to formulate the hypergeometric modification, which may be of self-independent interest. method 0.64 0.91 0.04 hedged possibility 0.94

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

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Original abstract

Let $X$ be any smooth Deligne-Mumford stack with projective coarse moduli, and $Y$ be a smooth complete intersection in $X$ associated with a direct sum of semi-positive line bundles. We will introduce a useful and broad class known as admissible series for discussing quantum Lefschetz theorem. For any admissible series on the Givental's Lagrangian cone of $X$, we will show that a hypergeometric modification of the series lies on the Lagrangian cone of $Y$. This confirms a prediction from Coates-Corti-Iritani-Tseng about the genus zero quantum Lefschetz theorem beyond convexity. In our quantum Lefschetz theorem, we use extended variables to formulate the hypergeometric modification, which may be of self-independent interest.

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