Abelian Vortices on Nodal and Cuspidal Curves

TL;DR

This paper calculates the Euler characteristics of moduli spaces of abelian vortices on singular curves, extending previous work to include cuspidal singularities, and aligns with string theory predictions about D-branes.

Contribution

It generalizes prior results by including cuspidal singularities in the computation of vortex moduli space Euler characteristics.

Findings

Euler characteristics computed for nodal and cuspidal curves

Results align with D2-D0 brane vortex models

Supports Gopakumar-Vafa conjecture

Abstract

We compute the Euler characteristics of the moduli spaces of abelian vortices on curves with nodal and cuspidal singularities. This generalizes our previous work where only nodes were taken into account. The result we obtain is again consistent with the expected reconciliation between the vortex picture of D2-D0 branes and the proposal by Gopakumar and Vafa.