Refined GW/Kronecker correspondence

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.

40 pages

References in corpus (4)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Cohomology of quiver moduli, functional equations, and integrality of Donaldson-Thomas type invariants
• Moduli of representations of quivers
• The canonical solutions of the Q-systems and the Kirillov-Reshetikhin conjecture