Moduli Spaces of Point Configurations and Plane Curve Counts

We identify certain Gromov-Witten invariants counting rational curves with given incidence and tangency conditions with the Euler characteristics 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.

Automated summary

By studying Gromov-Witten invariants of rational curves, we can identify and count the moduli space of point configurations using Euler characteristics. S. Fomin and G. Mikhalkin established a recurrence relation via tropicalization, which is applied in the moduli space using Donaldson-Thomas invariants.