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arXiv · 1908.09671

Secant varieties of toric varieties arising from simplicial complexes

M. Azeem Khadam·Mateusz Michałek·Piotr Zwiernik
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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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M. Azeem Khadam, Mateusz Michałek, Piotr Zwiernik. 2019-08-26. Secant varieties of toric varieties arising from simplicial complexes. https://arxiv.org/abs/1908.09671

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