Secant varieties of toric varieties arising from simplicial complexes

Khadam, Muhammad Azeem; Michalek, Mateusz; Zwiernik, Piotr

doi:http://dx.doi.org/10.1016/j.laa.2019.12.008

Secant varieties of toric varieties arising from simplicial complexes

Citation

Khadam MA, Michalek M, Zwiernik P. Secant varieties of toric varieties arising from simplicial complexes. Linear Algebra and its Applications. 2020 Mar 1; 588: 428-457. DOI: 10.1016/j.laa.2019.12.008

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 Q-Gorenstein varieties. We conclude providing the explicit description of the singular locus.