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MiS Preprint
81/2019

Secant varieties of toric varieties arising from simplicial complexes

Azeem Khadam, Mateusz Michałek and Piotr Zwiernik

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.

Received:
Aug 27, 2019
Published:
Sep 2, 2019
MSC Codes:
14E07, 14M25

Related publications

inJournal
2020 Repository Open Access
Muhammad Azeem Khadam, Mateusz Michałek and Piotr Zwiernik

Secant varieties of toric varieties arising from simplicial complexes

In: Linear algebra and its applications, 588 (2020), pp. 428-457