Secant varieties of toric varieties arising from simplicial complexes

M. Azeem Khadam*, Mateusz Michałek, Piotr Zwiernik

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)428-457
Number of pages30
JournalLinear Algebra and Its Applications
Volume588
DOIs
Publication statusPublished - 1 Mar 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • Cumulants
  • Secant variety
  • Segre-Veronese embedding
  • Simplicial complex
  • Singular locus

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