Higher genus Gromov–Witten invariants as genus zero invariants of symmetric products

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.We then express the pull back p * ψ i of the tautological ψ classes on M g,r (X), in terms of ψ classes and boundary divisors of M v →v (X).The boundary cycles of M η (X) are again products of similar stacks of étale correspondences.Further, there is a commutative diagram of evaluation maps M η (X) / / X r M g,r (X).

Locations

• arXiv (Cornell University) - PDF
• Annals of Mathematics - View - PDF