On toric Calabi-Yau hypersurfaces fibered by weighted K3 hypersurfaces

摘要

In response to a question of Reid, we find all anti-canonical Calabi-Yauhypersurfaces $X$ in toric weighted projective bundles over the projective linewhere the general fiber is a weighted K3 hypersurface. This gives a directgeneralization of Reid's discovery of the 95 families of weighted K3hypersurfaces. We also treat the case where $X$ is fibered over the plane withgeneral fiber a genus one curve in a weighted projective plane.