Secant varieties of toric varieties arising from simplicial complexes
Azeem Khadam, Mateusz Michałek, and Piotr Zwiernik
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Submission date: 27. Aug. 2019
published in: Linear algebra and its applications, 588 (2020), p. 428-457
DOI number (of the published article): 10.1016/j.laa.2019.12.008
MSC-Numbers: 14E07, 14M25
Link to arXiv:See the arXiv entry of this preprint.
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.