On deformations of toric varieties

2016/10/11 by Antonio Laface, Laface, Antonio, Manuel Melo +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1610.03455

openalex publication_date 2016/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

Citations

• Non-complete rational T-varieties of complexity one

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