کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4585292 | 1630530 | 2013 | 15 صفحه PDF | دانلود رایگان |
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.
Journal: Journal of Algebra - Volume 384, 15 June 2013, Pages 227-241