Mirror theorem for elliptic quasimap invariants

Abstract

We propose and prove a mirror theorem for the elliptic quasimap invariants of smooth Calabi–Yau complete intersections in projective spaces. This theorem, combined with the wall-crossing formula of Ciocan-Fontanine and Kim, implies mirror theorems of Zinger and Popa for the elliptic Gromov–Witten invariants of those varieties. This paper and the wall-crossing formula provide a unified framework for the mirror theory of rational and elliptic Gromov–Witten invariants.