Logarithmic connections on principal bundles over normal varieties

Abstract

Let X be a normal projective variety over an algebraically closed field of characteristic zero. Let D be a reduced Weil divisor on X. Let G be a reductive linear algebraic group. We study logarithmic connections on a principal G-bundle over X, which are singular along D. We give necessary and sufficient conditions for the existence of such a connection in terms of connections on associated vector bundles when the logarithmic tangent sheaf of X is locally free. The existence of a logarithmic connection on a principal bundle over a projective toric variety, singular along the boundary divisor, is shown to be equivalent to the existence of a torus equivariant structure on the bundle.