Moduli spaces of Higgs bundles on degenerating Riemann surfaces

Abstract

We prove a gluing theorem for solutions (A0,Φ0) of Hitchin's self-duality equations with logarithmic singularities on a rank-2 vector bundle over a noded Riemann surface Σ0 representing a boundary point of Teichmüller moduli space. We show that every nearby smooth Riemann surface Σ1 carries a smooth solution (A1,Φ1) of the self-duality equations, which may be viewed as a desingularization of (A0,Φ0).