{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/105891"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/105891","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On motivic Donaldson-Thomas invariants on the local projective plane","abstract":"Motivic Donaldson-Thomas (DT) invariant is a categorification of the classical DT invariant which contains more information of the local structure of a moduli space. In this thesis, we give three (partial) studies on the motivic DT invariants for various moduli spaces associated to the local projective plane (ωP2). In the first project, we give a construction of an orientation data for the stack of coherent sheaves on ωP2. In the second project, we construct a d-critical locus structure on Hilbn(ωP2), which is useful for recovering the computation of the motivic DT invariant associated to Hilbn(ωP2). Finally, we give some explicit computations on the motivic DT invariants associated to the stack of quiver representations, for a quiver related to ωP2 .","abstract_html":"Motivic Donaldson-Thomas (DT) invariant is a categorification of the classical DT invariant which contains more information of the local structure of a moduli space. In this thesis, we give three (partial) studies on the motivic DT invariants for various moduli spaces associated to the local projective plane (ωP2). In the first project, we give a construction of an orientation data for the stack of coherent sheaves on ωP2. In the second project, we construct a d-critical locus structure on Hilbn(ωP2), which is useful for recovering the computation of the motivic DT invariant associated to Hilbn(ωP2). Finally, we give some explicit computations on the motivic DT invariants associated to the stack of quiver representations, for a quiver related to ωP2 .","abstract_has_math":false,"creators":["Shi, Yun"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Katz, Sheldon","Nevins, Thomas","Bradlow, Steven","Haboush, William"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-11-26T20:58:36Z","date_published":"2019-11-26T20:58:36Z","updated_at":"2026-07-22T22:24:45Z","subjects":["motivic DT theory, local projective plane"],"languages":["en"],"rights":["Copyright 2019 Yun Shi"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/105891","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Katz, Sheldon","Nevins, Thomas","Bradlow, Steven","Haboush, William"]},{"key":"dc:creator","label":"Author","values":["Shi, Yun"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-11-26T20:58:36Z","2021-11-27T10:15:37Z","2019-07-03","2019-08"]},{"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":["motivic DT theory, local projective plane"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 Yun Shi"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/105891"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Motivic Donaldson-Thomas (DT) invariant is a categorification of the classical DT invariant which contains more information of the local structure of a moduli space. 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Finally, we give some explicit computations on the motivic DT invariants associated to the stack of quiver representations, for a quiver related to ωP2 .","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2021-08-01","The student, Yun Shi, accepted the attached license on 2019-07-01 at 18:27.","The student, Yun Shi, submitted this Dissertation for approval on 2019-07-01 at 19:16.","This Dissertation was approved for publication on 2019-07-03 at 15:28.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14127 on 2019-11-26 at 14:00:47","Made available in DSpace on 2019-11-26T20:58:36Z (GMT). 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In this thesis, we give three (partial) studies on the motivic DT invariants for various moduli spaces associated to the local projective plane (ωP2). In the first project, we give a construction of an orientation data for the stack of coherent sheaves on ωP2. In the second project, we construct a d-critical locus structure on Hilbn(ωP2), which is useful for recovering the computation of the motivic DT invariant associated to Hilbn(ωP2). Finally, we give some explicit computations on the motivic DT invariants associated to the stack of quiver representations, for a quiver related to ωP2 .","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2021-08-01","The student, Yun Shi, accepted the attached license on 2019-07-01 at 18:27.","The student, Yun Shi, submitted this Dissertation for approval on 2019-07-01 at 19:16.","This Dissertation was approved for publication on 2019-07-03 at 15:28.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14127 on 2019-11-26 at 14:00:47","Made available in DSpace on 2019-11-26T20:58:36Z (GMT). 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