Quantum Kirwan morphism and Gromov-Witten invariants of quotients II

TL;DR

This paper develops a quantum version of the Kirwan map linking equivariant and orbifold quantum cohomology for GIT quotients, and constructs virtual fundamental classes for related moduli spaces.

Contribution

It introduces a quantum Kirwan map for GIT quotients and constructs virtual fundamental classes on relevant moduli spaces, advancing the understanding of Gromov-Witten invariants.

Findings

Construction of virtual fundamental classes on moduli spaces.

Definition of a quantum Kirwan map for GIT quotients.

Intertwining of gauged and orbifold Gromov-Witten potentials.

Abstract

This is the second in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology of a smooth polarized complex projective variety with the action of a connected complex reductive group to the orbifold quantum cohomology of its geometric invariant theory quotient, and prove that it intertwines the genus zero gauged Gromov-Witten potential with the genus zero Gromov-Witten graph potential. In this part we construct virtual fundamental classes on the moduli spaces used in the construction of the quantum Kirwan map and the gauged Gromov-Witten potential.