EQUIVARIANT PRINCIPAL BUNDLES AND LOGARITHMIC CONNECTIONS ON TORIC VARIETIES

Let M be a smooth complex projective toric variety equipped with an action of a torus T, such that the complement D of the open T-orbit in M is a simple normal crossing divisor. Let G be a complex reductive affine algebraic group. We prove that an algebraic principal G-bundle E-G -> M admits a T-equivariant structure if and only if E-G admits a logarithmic connection singular over D. If E-H -> M is a T-equivariant algebraic principal H-bundle, where H is any complex affine algebraic group, then E-H in fact has a canonical integrable logarithmic connection singular over D.