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.
@article{ASNSP_2013_5_12_2_309_0, 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://www.numdam.org/item/ASNSP_2013_5_12_2_309_0/} }
TY - JOUR AU - Wong, Michael Lennox TI - Hecke modifications, wonderful compactifications and moduli of principal bundles JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2013 SP - 309 EP - 367 VL - 12 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2013_5_12_2_309_0/ LA - en ID - ASNSP_2013_5_12_2_309_0 ER -
%0 Journal Article %A Wong, Michael Lennox %T Hecke modifications, wonderful compactifications and moduli of principal bundles %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2013 %P 309-367 %V 12 %N 2 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2013_5_12_2_309_0/ %G en %F ASNSP_2013_5_12_2_309_0
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://www.numdam.org/item/ASNSP_2013_5_12_2_309_0/
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