On equivariant bundles and their moduli spaces

Abstract

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 $\mathcal{H}$-bundles on $X$, for an appropriate group $\mathcal{H}$ 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.

This work is based and expands the appendix of v1 of arXiv:1707.04448