Principal bundles on projective varieties and the Donaldson-Uhlenbeck compactification

Abstract

Let H be a semisimple algebraic group. We prove the semistable reduction theorem for μ-semistable principal H-bundles over a smooth projective variety X defined over the field C. When X is a smooth projective surface and H is simple, we construct the algebro-geometric Donaldson-Uhlenbeck compactification of the moduli space of μ-semistable principal H-bundles with fixed char-acteristic classes and describe its points. For large characteristic classes we show that the moduli space of μ-stable principal H-bundles is non-empty.