A mirror theorem for Gromov-Witten theory without convexity

Jun Wang

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A mirror theorem for Gromov-Witten theory without convexity

Jun Wang

Algebraic Geometry · Submitted 31 Oct 2019

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

The authors' main claim We prove a genus zero Givental-style mirror theorem for all complete intersections in proper toric Deligne-Mumford stacks, which provides an explicit slice called big $I-$function on Givental's Lagrangian cone for such targets.

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We prove a genus zero Givental-style mirror theorem for all complete intersections in proper toric Deligne-Mumford stacks, which provides an explicit slice called big $I-$function on Givental's Lagrangian cone for such targets. In particular, we remove a technical assumption called convexity needed in previous quantum Lefschetz theorem.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We prove a genus zero Givental-style mirror theorem for all complete intersections in proper toric Deligne-Mumford stacks, which provides an explicit slice called big $I-$function on Givental's Lagrangian cone for such targets.	contribution 0.64	0.96	0.93	asserted 1.00
s1	In particular, we remove a technical assumption called convexity needed in previous quantum Lefschetz theorem.	contribution 0.68	0.88	0.14	asserted 1.00

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Original abstract

We prove a genus zero Givental-style mirror theorem for all complete intersections in proper toric Deligne-Mumford stacks, which provides an explicit slice called big $I-$function on Givental's Lagrangian cone for such targets. In particular, we remove a technical assumption called convexity needed in previous quantum Lefschetz theorem.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

On the mirrors of low-degree del Pezzo surfaces
math.AG 2025-06 conditional novelty 7.0 of 10

The cohomological Hori-Vafa and Fanosearch mirrors of low-degree del Pezzo surfaces are shown to define categorical mirrors, with explicit mutation sequences connecting their exceptional collections to the Auroux-Katz...
Conjecture B for $X_{10}$ and its genus-two mirror
math.AG 2026-11 accept novelty 6.0 of 10

Conjecture B is proved unconditionally for the orbifold del Pezzo hypersurface X10 in weighted projective space P(1,2,3,5) via an S-extended GIT presentation and Wang's mirror theorem.

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6 arXiv papers cite this in 7 sentences

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Papers citing it · 4 sentences without a confident label

Uses its method or tool 1 paper

To compute the regularised quantum periods of $X_1$ and $X_2$, we argue as in [ref] , but using the mirror theorem for toric complete intersections due to J. Wang [ref] in place of the Quantum Lefschetz theorem and Givental's mirror theorem for toric manifolds.

Mirror Symmetry, Laurent Inversion and the Classification of $\mathbb{Q}$-Fano Threefolds · The varieties $X_1$ and $X_2$ are distinct · 0.89

Compares with it 1 paper

In a closely related independent approach, Wang [ref] also circumvents the convexity issues for complete intersections in toric stacks, showing that the a big $I$-function obtained from quasimap theory gives a slice of the Lagrangian cone in this case.

Gromov--Witten Invariants of Non-Convex Complete Intersections in Weighted Projective Stacks · Related Works · 0.89

Cites it as background 1 paper

Recent works by Guéré [ref] and Wang [ref] also address the computation of genus-zero Gromov–Witten theory of complete intersections when $E$ is not convex.

Quantum Serre duality for quasimaps · Removing the convexity hypothesis · 0.91

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