2010/10/05 by Michael Lennox Wong, Wong, Michael Lennox
Mathematics · #14D20 (Primary) #32G08 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14D20 #msc:32G08
paper · pdf · doi:10.48550/arxiv.1010.0877
45 pages; Section 1 substantially rewritten; other corrections and clarifications made
openalex publication_date 2010/10/05 · arxiv created 2011/08/23 · arxiv updated 2011/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.