Hecke Modifications, Wonderful Compactifications and Moduli of Principal Bundles
Abstract
In this paper, we obtain parametrizations of the moduli space of principal bundles over a compact Riemann surface using spaces of Hecke modifications in several cases. We begin with a discussion of Hecke modifications for principal bundles and give constructions of "universal" Hecke modifications of a fixed bundle of fixed type. This is followed by an overview of the construction of the "wonderful," or De Concini--Procesi, compactification of a semi-simple algebraic group of adjoint type. The compactification plays an important role in the deformation theory used in constructing the parametrizations. A general outline to construct parametrizations is given and verifications for specific structure groups are carried out.
Keywords
Cite
@article{arxiv.1010.0877,
title = {Hecke Modifications, Wonderful Compactifications and Moduli of Principal Bundles},
author = {Michael Lennox Wong},
journal= {arXiv preprint arXiv:1010.0877},
year = {2011}
}
Comments
45 pages; Section 1 substantially rewritten; other corrections and clarifications made