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https://hdl.handle.net/2142/86861
Description
Title
Fibered Calabi -Yau Varieties and Toric Varieties
Author(s)
Mullet, Joshua P.
Issue Date
2006
Doctoral Committee Chair(s)
Katz, Sheldon
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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 .
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