Smooth monomial Togliatti systems of cubics

Mateusz Michalek*, Rosa M. Miro-Roig

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

The goal of this paper is to prove the conjecture stated in [6], extending and correcting a previous conjecture of Ilardi [5], and classify smooth minimal monomial Togliatti systems of cubics in any dimension.

More precisely, we classify all minimal monomial artinian ideals I subset of k[x(0), ... ,x(n)] generated by cubics, failing the weak Lefschetz property and whose apolar cubic system I-1 defines a smooth toric variety. Equivalently, we classify all minimal monomial artinian ideals I subset of k[x(0), ... , x(n)] generated by cubics whose apolar cubic system I-1 defines a smooth toric variety satisfying at least a Laplace equation of order 2. Our methods rely on combinatorial properties of monomial ideals. (C) 2016 Published by Elsevier Inc.

Original languageEnglish
Pages (from-to)66-87
Number of pages22
JournalJournal of Combinatorial Theory Series A
Volume143
DOIs
Publication statusPublished - Oct 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • Osculating space
  • Weak Lefschetz property
  • Laplace equations
  • Toric threefold
  • WEAK LEFSCHETZ PROPERTY

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