Quantum Serre duality for quasimaps
Date
2022
Authors
Heath, Levi Nathaniel, author
Shoemaker, Mark, advisor
Cavalieri, Renzo, committee member
Gillespie, Maria, committee member
Gelfand, Martin, committee member
Journal Title
Journal ISSN
Volume Title
Abstract
Let X be a smooth variety or orbifold and let Z ⊆ X be a complete intersection defined by a section of a vector bundle E → 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∨. 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 nonconvex 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.