{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86776"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86776","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Moduli Questions for Augmented Bundles","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Hyeon, Donghoon"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Steven Bradlow","William Haboush"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:29Z","date_published":"2015-09-28T15:19:29Z","updated_at":"2026-07-22T22:26:27Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3017110"],"render_values":[{"text":"(MiAaPQ)AAI3017110","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86776","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Steven Bradlow","William Haboush"]},{"key":"dc:creator","label":"Author","values":["Hyeon, Donghoon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:29Z","10000-01-01","2001"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86776","(MiAaPQ)AAI3017110"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis consists of three parts. 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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.","Made available in DSpace on 2015-09-28T15:19:29Z (GMT). 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