Gromov-Witten invariants of P^2-stacks

TL;DR

This paper develops explicit recursive formulas to compute all genus 0 Gromov-Witten invariants of a specific P^2-stack, advancing the computational methods in the Gromov-Witten theory of stacks.

Contribution

It provides the first explicit recursions for genus 0 invariants of P^2-stacks, enabling comprehensive calculations beyond previous limited cases.

Findings

Derived explicit recursion relations for invariants.

Computed initial invariants by hand.

Determined all genus 0 invariants for the stack P^2_{D,2}.

Abstract

The Gromov-Witten theory of Deligne-Mumford stacks is a recent development, and hardly any computations have been done beyond 3-point genus 0 invariants. This paper provides explicit recursions which, together with some invariants computed by hand, determine all genus 0 invariants of the stack P^2_{D,2}. Here D is a smooth plane curve and P^2_{D,2} is locally isomorphic to the stack quotient [U/(Z/(2))], where U -> V \subset P^2 is a double cover branched along D \cap V. The introduction discusses an enumerative application of these invariants.