Geodesic
Hecke modifications, wonderful compactifications and moduli of principal bundles
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 2, pp. 309-367

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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.

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Classification : 14D20, 32G08 
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     author = {Wong, Michael Lennox},
     title = {Hecke modifications, wonderful compactifications and moduli of principal bundles},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {309--367},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 12},
     number = {2},
     year = {2013},
     mrnumber = {3114007},
     zbl = {1292.14011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_2_309_0/}
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Wong, Michael Lennox. Hecke modifications, wonderful compactifications and moduli of principal bundles. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 2, pp. 309-367. http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_2_309_0/