Refined GW/Kronecker correspondence

TL;DR

This paper explores the deep connection between Gromov-Witten invariants of weighted projective planes and Euler characteristics of bipartite quiver moduli spaces through the tropical vertex, providing explicit formulas and leveraging advanced geometric and algebraic techniques.

Contribution

It establishes a refined correspondence between Gromov-Witten invariants and quiver moduli, incorporating tropical geometry, wall-crossing formulas, and localization methods.

Findings

Derived explicit formulas for Gromov-Witten invariants.

Linked Gromov-Witten invariants with quiver Euler characteristics.

Utilized tropical vertex and wall-crossing techniques.

Abstract

Gromov-Witten invariants of weighted projective planes and Euler characteristics of moduli spaces of representations of bipartite quivers are related via the tropical vertex, a group of formal automorphisms of a torus. On the Gromov-Witten side, this uses the work of Gross, Pandharipande and Siebert. The quiver moduli side features quiver wall-crossing formulas, functional equations for Euler characteristics, and localization techniques. We derive several explicit formulas for Gromov-Witten invariants.