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

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

2010-09-17

arxiv.org/abs/1009.3485v2

Mathematics

Algebraic Geometry

36 pages

Scientific paper

Let $X$ be an irreducible smooth projective algebraic curve of genus $g \geq 2$ 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 a {\em semistable and stable parahoric} torsor under a certain Bruhat-Tits group scheme $\mathcal G$, construct the moduli space of semistable parahoric $\mathcal G$--torsors and 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 complete generalization of the earlier results of Mehta and Seshadri on parabolic vector bundles. The earlier version in the archiv had many typos and corrections which have been carried out in this version.

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