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Reconstruction theorems for genus 2 Gromov-Witten invariants

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arxiv 2210.04038 v1 pith:RWQ6ZF7J submitted 2022-10-08 math.AG

Thomas Wennink This is my paper · ORCID
classification math.AG
keywords genusgromov-witteninvariantsreconstructionblowncalculatedescendantfinite
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abstract

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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  1. Gromov-Witten theory of $\mathsf{Hilb}^n(\mathbb{C}^2)$ and Noether-Lefschetz theory of $\mathcal{A}_g$

    math.AG 2025-06 conditional novelty 8.0 of 10

    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.

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