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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
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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