Gromov-Witten invariants for varieties with C* action

TL;DR

This paper develops a method to compute Gromov-Witten invariants for smooth projective varieties with C* actions by reducing the problem to fixed loci, using GIT variation and stack constructions.

Contribution

It introduces a novel approach linking Gromov-Witten invariants to fixed loci via stacky GIT variation, enabling explicit calculations.

Findings

Reduction of Gromov-Witten invariants to fixed loci

Construction of building blocks for fixed loci

Explicit computation of contributions to the virtual fundamental class

Abstract

For any smooth projective variety with a C* action, we reduce the problem of computing its Gromov-Witten invariants to the similar problem for its fixed locus. Starting from the stacky version of variation of GIT for our variety, we construct the building blocks for the fixed loci of the moduli space of stable maps. We use this construction to compute their contribution to the virtual fundamental class.