2019/01/06 by V. Balaji, Balaji, V.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1901.01529
openalex publication_date 2019/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we answer two long-standing questions in the classification of G-torsors on curves for an almost simple, simply connected algebraic group G over the field of complex numbers. The first question is to give an intrinsic definition of (semi)stability for a G-torsor on an \em irreducible nodal curve and the second one is the construction of a flat degeneration of the moduli space of semistable G-torsors when the smooth curve degenerates to an irreducible nodal curve. A generalization of the classical Bruhat-Tits group schemes to two-dimensional regular local rings and an application of the geometric formulation of the McKay correspondence provide the key tools.