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 deforma- tions 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 toric varieties.
Gilberto Bini, Donatella Iacono (2020). Deformations of Calabi-Yau manifolds in Fano tori varieties. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 70, 1-14 [10.1007/s12215-020-00564-9].
Deformations of Calabi-Yau manifolds in Fano tori varieties
Gilberto Bini;
2020-01-01
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 HZF of infinitesimal deformations of Z in F to the functor of infinitesimal deforma- tions 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 toric varieties.
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