Secant varieties of toric varieties arising from simplicial complexes

2019/08/26 by Khadam, M. Azeem, Michałek, Mateusz, Zwiernik, Piotr
#14E07 #14M25 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1908.09671

Abstract

Motivated by the study of the secant variety of the Segre-Veronese variety we propose a general framework to analyze properties of the secant varieties of toric embeddings of affine spaces defined by simplicial complexes. We prove that every such secant is toric, which gives a way to use combinatorial tools to study singularities. We focus on the Segre-Veronese variety for which we completely classify their secants that give Gorenstein or \mathbb Q-Gorenstein varieties. We conclude providing the explicit description of the singular locus.

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