Reconstruction theorems for genus 2 Gromov-Witten invariants

TL;DR

This paper proves a reconstruction theorem for genus 2 Gromov-Witten invariants using Pixton's relations and computes specific invariants for blow-ups of the projective plane, advancing understanding in algebraic geometry.

Contribution

It introduces a new reconstruction theorem for genus 2 Gromov-Witten invariants based on Pixton's relations, extending previous genus 0 and 1 results.

Findings

Proved a reconstruction theorem for genus 2 invariants.

Calculated genus 2 Gromov-Witten invariants for blow-ups of P^2.

Extended the framework of Gromov-Witten theory to higher genus.

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.