Cones on ℂℙ²

Abstract

We proved in §3 that for a dense set of metrics the irreducible connections $\hat{M}$ in the moduli space form a smooth manifold. Now we examine the singular points {p₁,p₂, ... ,P _m } ⊆ M corresponding to reducible connections. We show that after a small perturbation of M, made either by hand or through a perturbation of the metric, a neighborhood of each singular point is homeomorphic to an open cone on ℂℙ². Furthermore, these homeomorphisms are smooth off the singular points.