Moduli of parahoric $\mathcal{G}$--torsors on a compact Riemann surface

Abstract

Let $X$ be an irreducible smooth projective algebraic curve of genus $g\ge 2$ over the ground field $\bc$ and let $G$ be a semisimple simply connected algebraic group. The aim of this paper is to introduce the notion of semistable and stable parahoric torsors under a certain Bruhat-Tits group scheme $\mathcal{G}$ and construct the moduli space of semistable parahoric $\mathcal{G}$--torsors; we also identify the underlying topological space of this moduli space with certain spaces of homomorphisms of Fuchsian groups into a maximal compact subgroup of $G$. The results give a generalization of the earlier results of Mehta and Seshadri on parabolic vector bundles. This is the final version of the accepted paper.

41 pages

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