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

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.