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A descendent relation in genus 2

Pasha Belorousski·Rahul Pandharipande
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Abstract

A new codimension 2 relation among descendent strata in the moduli space of stable, 3-pointed, genus 2 curves is found. The space of pointed admissible double covers is used in the calculation. The resulting differential equations satisfied by the genus 2 gravitational potentials of varieties in Gromov-Witten theory are described. These are analogous to the WDVV-equations in genus 0 and Getzler's equations in genus 1. As an application, genus 2 descendent invariants of the projective plane are determined, including the classical genus 2 Severi degrees.

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Pasha Belorousski, Rahul Pandharipande. 1998-03-17. A descendent relation in genus 2. https://arxiv.org/abs/math/9803072

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