Moduli spaces of point configurations and plane curve counts

TL;DR

This paper connects Gromov-Witten invariants counting rational curves with specific conditions to the topology of moduli spaces of point configurations, using tropicalization and Donaldson-Thomas invariants.

Contribution

It establishes a novel correspondence between enumerative geometry invariants and the Betti numbers of moduli spaces, linking tropical geometry and quiver invariants.

Findings

Recurrence relations for Gromov-Witten invariants derived from tropicalization.

Identification of Gromov-Witten invariants with Betti numbers of moduli spaces.

Use of Donaldson-Thomas invariants to realize geometric relations.

Abstract

We identify certain Gromov-Witten invariants counting rational curves with given incidence and tangency conditions with the Betti numbers of moduli spaces of point configurations in projective spaces. On the Gromov-Witten side, S. Fomin and G. Mikhalkin established a recurrence relation via tropicalization, which is realized on the moduli space side using Donaldson-Thomas invariants of subspace quivers.