2023/11/09 by Ludvig Olsson, Olsson, Ludvig, Stefan Reppen +3 · 1 citation
Mathematics · Medicine · #Advanced Algebra and Geometry #Advanced Neuroimaging Techniques and Applications #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2311.05326
openalex publication_date 2023/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove the existence of a projective good moduli space of principal G-bundles under nonconnected reductive group schemes G over a smooth projective curve C. We also prove that the moduli stack of G-bundles decomposes into finitely many substacks BunP each admitting a torsor BunGP→ BunP under a finite group, for some connected reductive group schemes GP over C. We use this for the second purpose of the article: for any constant connected reductive group G, the subset of essentially finite G-bundles in the moduli of degree 0 semistable G-bundles over C is not dense, unless G is a torus or the genus of C is smaller than 2. We do this by giving an upper bound on the dimension of the closure of the subset of essentially finite G-bundles.