Quantum Serre duality for quasimaps - Heath, Levi Nathaniel, author; Shoemaker, Mark, advisor; Cavalieri, Renzo, committee member; Gillespie, Maria, committee member; Gelfand, Martin, committee member (Colorado State University. Libraries, 2022)
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.