Moduli Questions for Augmented Bundles

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Hyeon, Donghoon

Contributors dc:contributor

• Steven Bradlow
• William Haboush

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3017110

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86776