Higher-genus Gromov-Witten invariants as genus 0 invariants of symmetric products

TL;DR

This paper presents a formula linking higher-genus Gromov-Witten invariants of a projective variety to genus 0 invariants of its symmetric product stack, simplifying calculations especially for the point case.

Contribution

It introduces a novel formula that expresses higher-genus invariants in terms of genus 0 invariants of symmetric products, providing a new computational approach.

Findings

Expressed higher-genus invariants via genus 0 invariants of symmetric products

Derived a new method for calculating Gromov-Witten invariants of a point

Connected Gromov-Witten invariants to symmetric group structure constants

Abstract

I prove a formula expressing the descendent genus g Gromov-Witten invariants of a projective variety X in terms of genus 0 invariants of its symmetric product stack S^{g+1}(X). When X is a point, the latter are structure constants of the symmetric group, and we obtain a new way of calculating the Gromov-Witten invariants of a point.