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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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