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

TL;DR

This paper computes genus 0 orbifold Gromov--Witten invariants for Calabi--Yau threefolds in weighted projective stacks, overcoming convexity limitations using quasimap wall-crossing and mirror symmetry techniques.

Contribution

It introduces a method to compute invariants without convexity assumptions using quasimap wall-crossing and provides explicit formulas and examples.

Findings

Explicit I-function formulas for various target spaces

Mirror theorem relating I- and J-functions via a mirror map

Computed invariants for multiple examples

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.