The Gromov Limit for Vortex Moduli Spaces

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.