Fibered Calabi -Yau Varieties and Toric Varieties

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 .

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Mullet, Joshua P.

Contributors dc:contributor

• Katz, Sheldon

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3223674

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86861