{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/16874"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/16874","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Quantum cohomology of a Hilbert scheme of a Hirzebruch surface","abstract":"In this thesis, we first use the ${\\mathbb C^*}^2$-action on the Hilbert scheme of two points on a Hirzebruch surface to compute all one-pointed and some two-pointed Gromov-Witten invariants via virtual localization, then making intensive use of the associativity law satisfied by quantum product, calculate other Gromov-Witten invariants sufficient for us to determine the structure of quantum cohomology ring of the Hilbert scheme. The novel point of this work is that we manage to avoid families of invariant curves with the freedom of choosing cycles to apply virtual localization method.","abstract_html":"In this thesis, we first use the <span class=\"etd-inline-math\">{\\mathbb C<sup>*</sup>}<sup>2</sup></span>-action on the Hilbert scheme of two points on a Hirzebruch surface to compute all one-pointed and some two-pointed Gromov-Witten invariants via virtual localization, then making intensive use of the associativity law satisfied by quantum product, calculate other Gromov-Witten invariants sufficient for us to determine the structure of quantum cohomology ring of the Hilbert scheme. The novel point of this work is that we manage to avoid families of invariant curves with the freedom of choosing cycles to apply virtual localization method.","abstract_has_math":true,"creators":["Fu, Yong"],"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 A.","Bradlow, Steven B.","Schenck, Henry K."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-08-20T18:00:31Z","date_published":"2010-08-20T18:00:31Z","updated_at":"2026-07-22T22:25:09Z","subjects":["Gromov-Witten invariants","quantum product"],"languages":["en"],"rights":["Copyright 2010 Yong Fu"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/16874","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Katz, Sheldon","Nevins, Thomas A.","Bradlow, Steven B.","Schenck, Henry K."]},{"key":"dc:creator","label":"Author","values":["Fu, Yong"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2010-08-20T18:00:31Z","2010-08"]},{"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":["Gromov-Witten invariants","quantum product"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2010 Yong Fu"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/16874"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis, we first use the ${\\mathbb C^*}^2$-action on the Hilbert scheme of two points on a Hirzebruch surface to compute all one-pointed and some two-pointed Gromov-Witten invariants via virtual localization, then making intensive use of the associativity law satisfied by quantum product, calculate other Gromov-Witten invariants sufficient for us to determine the structure of quantum cohomology ring of the Hilbert scheme. The novel point of this work is that we manage to avoid families of invariant curves with the freedom of choosing cycles to apply virtual localization method.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-07-13T17:46:30Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Fu_Yong.pdf: 551273 bytes, checksum: 3842d1e649e799b6f0df3d029e92ba6b (MD5)","Made available in DSpace on 2010-08-20T18:00:31Z (GMT). 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The novel point of this work is that we manage to avoid families of invariant curves with the freedom of choosing cycles to apply virtual localization method.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-07-13T17:46:30Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Fu_Yong.pdf: 551273 bytes, checksum: 3842d1e649e799b6f0df3d029e92ba6b (MD5)","Made available in DSpace on 2010-08-20T18:00:31Z (GMT). No. of bitstreams: 2 Fu_Yong.pdf: 551273 bytes, checksum: 3842d1e649e799b6f0df3d029e92ba6b (MD5) license.txt: 4055 bytes, checksum: 7b30b936bbf2c2ef1c16fd7dcadcf0ee (MD5)"],"dc:identifier":["http://hdl.handle.net/2142/16874"],"dc:language":["en"],"dc:rights":["Copyright 2010 Yong Fu"],"dc:subject":["Gromov-Witten invariants","quantum product"],"dc:title":["Quantum cohomology of a Hilbert scheme of a Hirzebruch surface"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:09Z"}