# The Gromov Limit for Vortex Moduli Spaces

## TL;DR

This paper extends the understanding of vortex moduli spaces by describing their Gromov limits for multiple sections, providing a way to compactify these spaces despite their non-compactness in smooth topology.

## Contribution

It generalizes previous descriptions to multiple sections with an adiabatic parameter and constructs a Gromov limit to compactify the moduli space of vortices.

## Key findings

- Moduli space is topologically independent of the adiabatic constant s.
- The moduli space is not compact in the smooth topology.
- A Gromov limit provides a compactification of the vortex moduli space.

## Abstract

We generalize the descriptions of vortex moduli spaces in \cite{Br} to more than one section with adiabatic constant $s$. The moduli space is topologically independent of $s$ but is not compact with respect to $C^\infty$ topology. Following \cite{PW}, we construct a Gromov limit for vortices of fixed energy, an attempt to compactify the moduli space.