Secant Cumulants and Toric Geometry

Mateusz Michalek*, Luke Oeding, Piotr Zwiernik

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We study the secant line variety of the Segre product of projective spaces using special cumulant coordinates adapted for secant varieties. We show that the secant variety is covered by open normal toric varieties. We prove that in cumulant coordinates its ideal is generated by binomial quadrics. We present new results on the local structure of the secant variety. In particular, we show that it has rational singularities and we give a description of the singular locus. We also classify all secant varieties that are Gorenstein. Moreover, generalizing [31], we obtain analogous results for the tangential variety.

Original languageEnglish
Pages (from-to)4019-4063
Number of pages45
JournalINTERNATIONAL MATHEMATICS RESEARCH NOTICES
Issue number12
DOIs
Publication statusPublished - 2015
MoE publication typeA1 Journal article-refereed

Keywords

  • GROUP-BASED MODELS
  • SEGRE VARIETIES
  • IDEALS
  • POLYTOPES
  • VERONESE
  • GRAPHS

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