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Research article - Algebraic geometry
On equivariant bundles and their moduli spaces
Chiara Damiolini1, 2
1 Department of Mathematics, University of Pennsylvania, Philadelphia, USA
2 Department of Mathematics, University of Texas at Austin, Austin, USA
Comptes Rendus. Mathématique, Volume 362 (2024), pp. 55-62.

Let G be an algebraic group and Γ a finite subgroup of automorphisms of G. Fix also a possibly ramified Γ-covering X ˜→X. In this setting one may define the notion of (Γ,G)-bundles over X ˜ and, in this paper, we give a description of these objects in terms of ℋ-bundles on X, for an appropriate group ℋ over X which depends on the local type of the (Γ,G)-bundles we intend to parametrize. This extends, and along the way clarifies, an earlier work of Balaji and Seshadri.

Soit G un groupe algébrique et Γ un sous-groupe fini d’automorphismes de G. Nous fixons également un Γ-revêtement éventuellement ramifié X ˜→X. Dans ce cadre, on peut définir la notion de (Γ,G)-fibré sur X ˜ et, dans cet article, nous donnons une description de ces objets en termes de ℋ-fibrés sur X, pour un groupe ℋ sur X qui dépend du type local des (Γ,G)-fibrés que nous avons l’intention de paramétrer. Ceci étend, et en même temps clarifie, un travail antérieur de Balaji et Seshadri.

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DOI: 10.5802/crmath.524

Chiara Damiolini 1, 2

1 Department of Mathematics, University of Pennsylvania, Philadelphia, USA
2 Department of Mathematics, University of Texas at Austin, Austin, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Chiara Damiolini. On equivariant bundles and their moduli spaces. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 55-62. doi : 10.5802/crmath.524. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.524/

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