On toric Calabi-Yau hypersurfaces fibered by weighted K3 hypersurfaces

الأصل · EN

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.