On toric Calabi-Yau hypersurfaces fibered by weighted K3 hypersurfaces

Details On toric Calabi-Yau hypersurfaces fibered by weighted K3 hypersurfaces On toric Calabi-Yau hypersurfaces fibered by weighted K3 hypersurfaces

2006-11-11

arxiv.org/abs/math/0611338v1

Mathematics

Algebraic Geometry

Scientific paper

In response to a question of Reid, we find all anti-canonical Calabi-Yau hypersurfaces $X$ in toric weighted projective bundles over the projective line where the general fiber is a weighted K3 hypersurface. This gives a direct generalization of Reid's discovery of the 95 families of weighted K3 hypersurfaces. We also treat the case where $X$ is fibered over the plane with general fiber a genus one curve in a weighted projective plane.

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