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arXiv · 2005.05582

Deformations of Calabi-Yau manifolds in Fano toric varieties

Gilberto Bini·Donatella Iacono
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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.

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Gilberto Bini, Donatella Iacono. 2020-05-12. Deformations of Calabi-Yau manifolds in Fano toric varieties. https://doi.org/10.1007/s12215-020-00564-9

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