{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/101520"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/101520","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Stratifications of representations and cyclic quivers","abstract":"DSpace SAF Submission Ingestion Package generated from Vireo submission #12706 on 2018-09-27 at 10:46:21","abstract_html":"DSpace SAF Submission Ingestion Package generated from Vireo submission #12706 on 2018-09-27 at 10:46:21","abstract_has_math":false,"creators":["Ochoa de Alaiza Gracia, Itziar"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Nevins, Thomas","Loja Fernandes, Rui","Yong, Alexander","Dodd, Christopher"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-27T16:17:36Z","date_published":"2018-09-27T16:17:36Z","updated_at":"2026-07-22T22:24:40Z","subjects":["Representations, quivers."],"languages":["en"],"rights":["Copyright 2018 by Itziar Ochoa de Alaiza Gracia. All rights reserved."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/101520","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Nevins, Thomas","Loja Fernandes, Rui","Yong, Alexander","Dodd, Christopher"]},{"key":"dc:creator","label":"Author","values":["Ochoa de Alaiza Gracia, Itziar"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-09-27T16:17:36Z","2018-07-06","2018-08"]},{"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":["Representations, quivers."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 by Itziar Ochoa de Alaiza Gracia. All rights reserved."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/101520"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["DSpace SAF Submission Ingestion Package generated from Vireo submission #12706 on 2018-09-27 at 10:46:21","Made available in DSpace on 2018-09-27T16:17:36Z (GMT). No. of bitstreams: 2 OCHOADEALAIZAGRACIA-DISSERTATION-2018.pdf: 572835 bytes, checksum: 2ec87f6e002f8524777409d7cb5d7dcf (MD5) LICENSE.txt: 4226 bytes, checksum: abfff410eef9312fe29beaf2e0ecd227 (MD5) Previous issue date: 2018-07-06","Given an algebraic variety $X$ with an action of a reductive group $G$, geometric invariant theory splits $X$ as the disjoint union $X=X^{ss}\\sqcup X^{un}$ of the semistable and unstable locus. The Kirwan-Ness stratification refines $X$ even more by describing $X^{un}$ as a disjoint union of strata $X^{un}=\\displaystyle\\sqcup_{\\beta\\in\\textsf{KN}} S_\\beta$ detemined by 1-parameter subgroups $\\beta$. In this thesis we study the 1-parameter subgroups that determine the Kirwan-Ness stratifications of representations. We will describe an algorithm that finds the $\\beta$'s and we show that such algorithm can be simplified when our space is of the form $T^*V$ where $V$ is a vector space. We go on to investigate more deeply the 1-parameter subgroups in the case of the space of representations $\\text{Rep}(Q,v)$ of a cyclic quiver $Q$.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms","The student, Itziar Ochoa de Alaiza Gracia, accepted the attached license on 2018-07-02 at 15:46.","The student, Itziar Ochoa de Alaiza Gracia, submitted this Dissertation for approval on 2018-07-02 at 15:47.","This Dissertation was approved for publication on 2018-07-06 at 09:02."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Stratifications of representations and cyclic quivers"]}]}],"canonical_facts":{"dc:contributor":["Nevins, Thomas","Loja Fernandes, Rui","Yong, Alexander","Dodd, Christopher"],"dc:creator":["Ochoa de Alaiza Gracia, Itziar"],"dc:date":["2018-09-27T16:17:36Z","2018-07-06","2018-08"],"dc:description":["DSpace SAF Submission Ingestion Package generated from Vireo submission #12706 on 2018-09-27 at 10:46:21","Made available in DSpace on 2018-09-27T16:17:36Z (GMT). No. of bitstreams: 2 OCHOADEALAIZAGRACIA-DISSERTATION-2018.pdf: 572835 bytes, checksum: 2ec87f6e002f8524777409d7cb5d7dcf (MD5) LICENSE.txt: 4226 bytes, checksum: abfff410eef9312fe29beaf2e0ecd227 (MD5) Previous issue date: 2018-07-06","Given an algebraic variety $X$ with an action of a reductive group $G$, geometric invariant theory splits $X$ as the disjoint union $X=X^{ss}\\sqcup X^{un}$ of the semistable and unstable locus. The Kirwan-Ness stratification refines $X$ even more by describing $X^{un}$ as a disjoint union of strata $X^{un}=\\displaystyle\\sqcup_{\\beta\\in\\textsf{KN}} S_\\beta$ detemined by 1-parameter subgroups $\\beta$. In this thesis we study the 1-parameter subgroups that determine the Kirwan-Ness stratifications of representations. We will describe an algorithm that finds the $\\beta$'s and we show that such algorithm can be simplified when our space is of the form $T^*V$ where $V$ is a vector space. We go on to investigate more deeply the 1-parameter subgroups in the case of the space of representations $\\text{Rep}(Q,v)$ of a cyclic quiver $Q$.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms","The student, Itziar Ochoa de Alaiza Gracia, accepted the attached license on 2018-07-02 at 15:46.","The student, Itziar Ochoa de Alaiza Gracia, submitted this Dissertation for approval on 2018-07-02 at 15:47.","This Dissertation was approved for publication on 2018-07-06 at 09:02."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/101520"],"dc:language":["en"],"dc:rights":["Copyright 2018 by Itziar Ochoa de Alaiza Gracia. All rights reserved."],"dc:subject":["Representations, quivers."],"dc:title":["Stratifications of representations and cyclic quivers"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:40Z"}