Quantum Serre duality for quasimaps

TL;DR

This paper establishes a quantum Serre duality for quasimap invariants of complete intersections, simplifying previous results and extending them to non-convex cases, thereby connecting Gromov-Witten invariants and quasimaps.

Contribution

It proves a quantum Serre duality for quasimap invariants, including non-convex complete intersections, and links it to Gromov-Witten theory via wall-crossing techniques.

Findings

Quantum Serre duality for quasimap invariants proved.

Comparison simplifies and extends to non-convex complete intersections.

Results connect quasimap invariants with Gromov-Witten invariants without convexity assumptions.

Abstract

Let $X$ be a smooth variety or orbifold and let $Z \subseteq X$ be a complete intersection defined by a section of a vector bundle $E \to X$. Originally proposed by Givental, quantum Serre duality refers to a precise relationship between the Gromov--Witten invariants of $Z$ and those of the dual vector bundle $E^\vee$. In this paper we prove a quantum Serre duality statement for quasimap invariants. In shifting focus to quasimaps, we obtain a comparison which is simpler and which also holds for non-convex complete intersections. By combining our results with the wall-crossing formula developed by Zhou, we recover a quantum Serre duality statement in Gromov-Witten theory without assuming convexity.