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

Kevin Costello
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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.

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Kevin Costello. 2003-12-17. Higher-genus Gromov-Witten invariants as genus 0 invariants of symmetric products. https://arxiv.org/abs/math/0303387

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