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Equivariant principal bundles and logarithmic connections on toric varieties
Published in University of California, Berkeley
2016
Volume: 280

Issue: 2
Pages: 315 - 325
Abstract
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 EG → M admits a T-equivariant structure if and only if EG admits a logarithmic connection singular over D. If EH → M is a T-equivariant algebraic principal H-bundle, where H is any complex affine algebraic group, then EH in fact has a canonical integrable logarithmic connection singular over D.