Hecke Modifications, Wonderful Compactifications and Moduli of Principal Bundles
Hecke Modifications, Wonderful Compactifications and Moduli of Principal Bundles
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Hecke 修正、精彩紧化和主丛模
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发表时间：
2010
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通讯作者：
Michael Lennox Wong
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作者：
Michael Lennox Wong
本文利用Hecke修改空间在几种情况下得到了紧致Riemann曲面上主丛模空间的参数化。我们开始讨论主丛的Hecke修改，并给出固定型固定丛的“泛”Hecke修改的构造。其次是概述建设的“精彩”，或德Concini-Procesi，紧化的半简单代数群的伴随类型。紧化在构造参数化的变形理论中起着重要的作用。给出了构造参数化的一般框架，并对具体的结构群进行了验证。
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.