Deformations of Calabi-Yau manifolds in Fano toric varieties

Abstract

In this article, we investigate deformations of a Calabi-Yau manifold Z in a toric variety F , possibly not smooth. In particular, we prove that the forgetful morphism from the Hilbert functor H F Z of infinitesimal deformations of Z in F to the functor of infinitesimal deformations of Z is smooth. This implies the smoothness of H F Z at the corresponding point in the Hilbert scheme. Moreover, we give some examples and include some computations on the Hodge numbers of Calabi-Yau manifolds in Fano toric varieties.