Deformations of Calabi-Yau manifolds in Fano toric varieties

Gilberto Bini, Donatella Iacono
2020 Rendiconti del circolo matematico di Palermo  
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 HZF of infinitesimal deformations of Z in F to the functor of infinitesimal deformations of Z is smooth. This implies the smoothness of HZF 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
more » ... anifolds in Fano toric varieties.
doi:10.1007/s12215-020-00564-9 fatcat:cf2ga22xufeytgrvjxpvp4tvae