Smooth monomial Togliatti systems of cubics

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:143

Article

Michalek, Mateusz^1,2  Miro-Roig, Rosa M.¹ 

[1] Fac Matemat, Dept Algebra & Geometria, Gran Via Corts Catalanes 585, Barcelona 08007, Spain

[2] Polish Acad Sci, Math Inst, PL-00956 Warsaw, Poland

关键词: Osculating space;    Weak Lefschetz property;    Laplace equations;    Toric threefold;   

DOI  :  10.1016/j.jcta.2016.05.004

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free