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arXiv · 1610.03455

On deformations of toric varieties

Antonio Laface·Manuel Melo
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Abstract

Let X be a smooth complete toric variety. We describe the Altmann-Ilten-Vollmert equivariant deformations of toric varieties in the language of Cox rings. More precisely we construct one parameters families of deformations of X, such that the total space of the deformation is a T-variety of complexity one defined by a trinomial equation, and the deformation map is equivariant with respect to the torus action. Moreover we show that the images of all these families via the Kodaira-Spencer map form a basis of the vector space H1(X,T_X).

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Antonio Laface, Manuel Melo. 2016-10-11. On deformations of toric varieties. https://arxiv.org/abs/1610.03455

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