Biswas, IndranilMuñoz, VicenteSánchez Hernández, Jonathan2023-06-192023-06-192013-060021-869310.1016/j.jalgebra.2013.02.039https://hdl.handle.net/20.500.14352/33320Let 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 groupengjournal articlehttp://www.sciencedirect.com/science/article/pii/S002186931300152Xhttp://www.sciencedirect.com/restricted access51Toric varietyEquivariant bundleLogarithmic connectionG-pairMatemáticas (Matemáticas)12 Matemáticas