Asymptotic geometry in moduli of nonlinear Abelian vortices

The moduli spaces of Abelian vortices on a Riemann surface X are Kaehler
manifolds generalising the symmetric products of X.  For nonlinear vortices, these spaces may come with a natural boundary -- even if X is compact. Then an interesting (but difficult) problem is to understand the asymptotic geometry near such boundary ends. I will present recent results in this direction, with special focus on the simplest nontrivial example where the asymptotic geometry can be
described explicitly (joint work with M. Speight).