Please use this identifier to cite or link to this item: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/9141
Title: G-connections on principal bundles over complete G-varieties
Authors: Khan, Bivas
PODDAR, MAINAK 
Dept. of Mathematics
Keywords: Principal bundle
Group action
Complete variety
G-connection
Toric variety
2025
2024-OCT-WEEK2
TOC-OCT-2024
Issue Date: Jan-2025
Publisher: Elsevier B.V.
Citation: Journal of Pure and Applied Algebra, 229(01), 107816.
Abstract: Let X be a complete variety over an algebraically closed field k of characteristic zero, equipped with an action of an algebraic group G. Let H be a reductive group. We study the notion of G-connection on a principal H-bundle. We give necessary and sufficient criteria for the existence of G-connections extending the Atiyah-Weil type criterion for holomorphic connections obtained by Azad and Biswas. We also establish a relationship between the existence of G-connection and equivariant structure on a principal H-bundle, under the assumption that G is semisimple and simply connected. These results have been obtained by Biswas et al. when the underlying variety is smooth.
URI: https://doi.org/10.1016/j.jpaa.2024.107816
http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/9141
ISSN: 1873-1376
0022-4049
Appears in Collections:JOURNAL ARTICLES

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