Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

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


Authors: V. Balaji and C. S. Seshadri
Journal: J. Algebraic Geom. 24 (2015), 1-49
DOI: https://doi.org/10.1090/S1056-3911-2014-00626-3
Published electronically: February 24, 2014
MathSciNet review: 3275653
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Abstract: Let $X$ be an irreducible smooth projective algebraic curve of genus $g \geq 2$ over the ground field $\mathbb {C}$, 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 to 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.


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V. Balaji
Affiliation: Chennai Mathematical Institute SIPCOT IT Park, Siruseri-603103, India
Email: balaji@cmi.ac.in

C. S. Seshadri
Affiliation: Chennai Mathematical Institute SIPCOT IT Park, Siruseri-603103, India
Email: css@cmi.ac.in

Received by editor(s): July 9, 2011
Published electronically: February 24, 2014
Additional Notes: The research of the first author was partially supported by the J. C. Bose Research grant.
Dedicated: Dedicated to Professor K. Chandrasekharan in admiration
Article copyright: © Copyright 2014 University Press, Inc.
The copyright for this article reverts to public domain 28 years after publication.