Secant varieties of toric varieties arising from simplicial complexes

Citació

  • 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

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Descripció

  • Resum

    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.

  • DOI

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

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