Year: 2021
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Heath, Levi, Shoemaker, Mark
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4287080071