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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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