2025/05/29 by G. Barajas, Barajas, Guillermo
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2505.23488
Let X be a compact Riemann surface, Γ a finite group of automorphisms of X and G a connected reductive complex Lie group with center Z. If we equip this data with a homomorphism θ:Γ\toAut(G) and a 2-cocycle c:Γ×Γ→ Z, there is a notion of (θ,c)-twisted Γ-equivariant G-bundle over X. The aim of this paper is to construct a coarse moduli space of isomorphism classes of polystable (θ,c)-twisted equivariant G-bundles over X, according to the definition of polystability given by García-Prada--Gothen--Mundet i Riera. This generalizes the well-known construction of the moduli space of G-bundles given by Ramanathan. It also gives, in particular, a GIT construction of the moduli space of Γ-equivariant G-bundles, and the moduli space of G-bundles for G non-connected by our joint work with García-Prada, Gothen and Mundet i Riera -- complementing the construction of a projective good moduli space for the moduli stack of G-bundles given by Olsson--Reppen--Tajakka.