{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86861"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86861","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Fibered Calabi -Yau Varieties and Toric Varieties","abstract":"We consider the problem of constructing K3-fibered and elliptically fibered Calabi-Yau threefolds over P1 and P2 respectively. We first show how to write weighted projective space bundles as toric varieties. We then find necessary and sufficient conditions for the anti-canonical linear systems of these bundles to have quasi-smooth members. These quasi-smooth members are Calabi-Yau varieties over the base whose general fiber is also a Calabi-Yau variety. A computer calculation finds all 3,723 families of weighted K3-fibered toric Calabi-Yau threefold hypersurfaces over P2 and all 92 of families elliptically fibered toric Calabi-Yau threefold hypersurfaces over P1 .","abstract_html":"We consider the problem of constructing K3-fibered and elliptically fibered Calabi-Yau threefolds over P1 and P2 respectively. We first show how to write weighted projective space bundles as toric varieties. We then find necessary and sufficient conditions for the anti-canonical linear systems of these bundles to have quasi-smooth members. These quasi-smooth members are Calabi-Yau varieties over the base whose general fiber is also a Calabi-Yau variety. A computer calculation finds all 3,723 families of weighted K3-fibered toric Calabi-Yau threefold hypersurfaces over P2 and all 92 of families elliptically fibered toric Calabi-Yau threefold hypersurfaces over P1 .","abstract_has_math":false,"creators":["Mullet, Joshua P."],"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"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:54Z","date_published":"2015-09-28T15:19:54Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3223674"],"render_values":[{"text":"(MiAaPQ)AAI3223674","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86861","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Katz, Sheldon"]},{"key":"dc:creator","label":"Author","values":["Mullet, Joshua P."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:54Z","10000-01-01","2006"]},{"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/2142/86861","(MiAaPQ)AAI3223674"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We consider the problem of constructing K3-fibered and elliptically fibered Calabi-Yau threefolds over P1 and P2 respectively. We first show how to write weighted projective space bundles as toric varieties. We then find necessary and sufficient conditions for the anti-canonical linear systems of these bundles to have quasi-smooth members. These quasi-smooth members are Calabi-Yau varieties over the base whose general fiber is also a Calabi-Yau variety. A computer calculation finds all 3,723 families of weighted K3-fibered toric Calabi-Yau threefold hypersurfaces over P2 and all 92 of families elliptically fibered toric Calabi-Yau threefold hypersurfaces over P1 .","Made available in DSpace on 2015-09-28T15:19:54Z (GMT). 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We first show how to write weighted projective space bundles as toric varieties. We then find necessary and sufficient conditions for the anti-canonical linear systems of these bundles to have quasi-smooth members. These quasi-smooth members are Calabi-Yau varieties over the base whose general fiber is also a Calabi-Yau variety. A computer calculation finds all 3,723 families of weighted K3-fibered toric Calabi-Yau threefold hypersurfaces over P2 and all 92 of families elliptically fibered toric Calabi-Yau threefold hypersurfaces over P1 .","Made available in DSpace on 2015-09-28T15:19:54Z (GMT). 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