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Higher genus Gromov-Witten invariants as genus zero invariants of symmetric products. (English) Zbl 1209.14046

Summary: We 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.

MSC:

14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
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