Instanton moduli spaces on non-Kählerian surfaces. Holomorphic models around the reduction loci

Let MM be a moduli space of polystable rank 2-bundles with fixed determinant (a moduli space of PU(2)-instantons) on a Gauduchon surface with pg=0pg=0 and b1=1b1=1. We study the holomorphic structure of MM around a circle TT of regular reductions. Our model space is a “blowup flip passage”, which is a manifold with boundary whose boundary is a projective fibration, and whose interior comes with a natural complex structure.We prove that a neighborhood of the boundary of the blowup MˆT of MM at TT can be smoothly identified with a neighborhood of the boundary of a “flip passage” Qˆ, the identification being holomorphic on int(Qˆ).