The genus 1 divisor Gromov-Witten invariant of Hilb^n(C^2) is expressed through traces of quantum multiplication and equals the Eisenstein generating function that also governs Noether-Lefschetz cycles on A_g.
Reconstruction theorems for genus 2 Gromov-Witten invariants
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We use Pixton's relations to prove a reconstruction theorem for genus 2 Gromov-Witten invariants in the style of Kontsevich-Manin (genus 0) and Getzler (genus 1). We also calculate genus 2 (descendant) Gromov-Witten invariants of $\mathbb{P}^2$ blown up at a finite number of points in general position.
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Gromov-Witten theory of $\mathsf{Hilb}^n(\mathbb{C}^2)$ and Noether-Lefschetz theory of $\mathcal{A}_g$
The genus 1 divisor Gromov-Witten invariant of Hilb^n(C^2) is expressed through traces of quantum multiplication and equals the Eisenstein generating function that also governs Noether-Lefschetz cycles on A_g.