%0 Journal Article
%A Biswas, Indranil
%A Muñoz, Vicente
%A Sánchez Hernández, Jonathan
%T Equivariant vector bundles and logarithmic connections on toric varieties
%D 2013
%@ 0021-8693
%U https://hdl.handle.net/20.500.14352/33320
%X Let X be a smooth complete complex toric variety such that the boundary is a simple normal crossing divisor, and let E be a holomorphic vector bundle on X. We prove that the following three statements are equivalent: The holomorphic vector bundle E admits an equivariant structure. The holomorphic vector bundle E admits an integrable logarithmic connection singular over D. The holomorphic vector bundle E admits a logarithmic connection singular over D. We show that an equivariant vector bundle on X has a tautological integrable logarithmic connection singular over D. This is used in computing the Chern classes of the equivariant vector bundles on X. We also prove a version of the above result for holomorphic vector bundles on log parallelizable G-pairs (X, D), where G is a simply connected complex affine algebraic group
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