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arXiv · 2409.06193

Gromov--Witten Invariants of Non-Convex Complete Intersections in Weighted Projective Stacks

Felix Janda·Nawaz Sultani·Yang Zhou
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Abstract

In this paper we compute genus 0 orbifold Gromov--Witten invariants of Calabi--Yau threefold complete intersections in weighted projective stacks, regardless of convexity conditions. The traditional quantumn Lefschetz principle may fail even for invariants with ambient insertions. Using quasimap wall-crossing, we are able to compute invariants with insertions from a specific subring of the Chen--Ruan cohomology, which contains all the ambient cohomology classes. Quasimap wall-crossing gives a mirror theorem expressing the I-function in terms of the J-function via a mirror map. The key of this paper is to find a suitable GIT presentation of the target space, so that the mirror map is invertible. An explicit formula for the I-function is given for all those target spaces and many examples with explicit computations of invariants are provided.

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Felix Janda, Nawaz Sultani, Yang Zhou. 2024-09-10. Gromov--Witten Invariants of Non-Convex Complete Intersections in Weighted Projective Stacks. https://arxiv.org/abs/2409.06193

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