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 Title: Moduli Questions for Augmented Bundles Author(s): Hyeon, Donghoon Doctoral Committee Chair(s): Steven Bradlow; William Haboush Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: This thesis consists of three parts. In the first part, we construct the moduli scheme for principal bundles over an arbitrary projective scheme. In the second, we establish a bijective correspondence between the analytic master space and the algebraic master space for Bradlow pairs. We also consider the master stack for Bradlow pairs, and show that it is a nontrivial line bundle over the moduli stack. In the third, we prove that the stability for certain augmented bundles is preserved by the direct image functor when the covering is etale. Also, we study the relation between the spectral curve associated to a Higgs bundle and the spectral curve associated to the direct image of it. Issue Date: 2001 Type: Text Language: English Description: 131 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001. URI: http://hdl.handle.net/2142/86776 Other Identifier(s): (MiAaPQ)AAI3017110 Date Available in IDEALS: 2015-09-28 Date Deposited: 2001
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