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Equivariant vector bundles and logarithmic connections on toric varieties

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Biswas, Indranil and Muñoz, Vicente and Sánchez Hernández, Jonathan (2013) Equivariant vector bundles and logarithmic connections on toric varieties. Journal of Algebra, 384 . pp. 227-241. ISSN 0021-8693

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Official URL: http://www.sciencedirect.com/science/article/pii/S002186931300152X


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Abstract

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


Item Type:Article
Uncontrolled Keywords:Toric variety; Equivariant bundle; Logarithmic connection; G-pair
Subjects:Sciences > Mathematics
ID Code:22154
Deposited On:28 Jun 2013 11:14
Last Modified:12 Dec 2018 15:12

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