A criterion for holomorphic extension of principal bundles

Abstract

Let G be a complex affine algebraic group, and let E_G be a holomorphic principal G-bundle on the complement M \ S, where S is a closed complex analytic subset, of complex codimension at least two, of a connected complex manifold M. We give a criterion for E_G to extend to M as a holomorphic principal G-bundle. Two applications of this criterion are given.