On equivariant bundles and their moduli spaces

Damiolini, Chiara

Comptes Rendus. Mathématique, Tome 362 (2024) no. G1, pp. 55-62

Let $G$ be an algebraic group and $\Gamma$ a finite subgroup of automorphisms of $G$. Fix also a possibly ramified $\Gamma$-covering $\tilde{X}\to X$. In this setting one may define the notion of $(\Gamma ,G)$-bundles over $\tilde{X}$ and, in this paper, we give a description of these objects in terms of $\mathscr{H}$-bundles on $X$, for an appropriate group $\mathscr{H}$ over $X$ which depends on the local type of the $(\Gamma ,G)$-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 $\Gamma$ un sous-groupe fini d’automorphismes de $G$. Nous fixons également un $\Gamma$-revêtement éventuellement ramifié $\tilde{X}\to X$. Dans ce cadre, on peut définir la notion de $(\Gamma ,G)$-fibré sur $\tilde{X}$ et, dans cet article, nous donnons une description de ces objets en termes de $\mathscr{H}$-fibrés sur $X$, pour un groupe $\mathscr{H}$ sur $X$ qui dépend du type local des $(\Gamma ,G)$-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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