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 .
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign