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arXiv · 1901.01529

Torsors on semistable curves and degenerations

V. Balaji
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Abstract

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.

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V. Balaji. 2019-01-06. Torsors on semistable curves and degenerations. https://arxiv.org/abs/1901.01529

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