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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

PDF
Restringido a Repository staff only 220kB |

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 |
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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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