Smooth monomial Togliatti systems of cubics

2013/10/09 by Mateusz Michałek, Michałek, Mateusz, Rosa-Maria Miró-Roig +1 · 1 citation
Mathematics · #13E10 #14M25 #14N05 #14N15 #53A20 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #math.AG #math.CO #msc:13E10 #msc:14M25 #msc:14N05 #msc:14N15 #msc:53A20

paper · pdf · doi:10.48550/arxiv.1310.2529

arxiv created 2016/05/18 · arxiv updated 2016/05/19

Abstract

The goal of this paper is to solve the conjecture stated in a paper of Mezzetti, Miró-Roig, Ottaviani and classify all smooth minimal monomial Togliatti systems of cubics. More precisely, we classify all minimal monomial artinian ideals generated by cubics, failing the weak Lefschetz property and whose apolar cubic system defines a smooth toric variety or, equivalently, we classify all minimal monomial artinian ideals generated by cubics whose apolar cubic system defines a smooth toric variety satisfying at least a Laplace equation of order 2.

Cited by

• The Weak Lefschetz Property for Tensor Products of Artinian Monomial Algebras and Its Applications to Lollipop Graphs

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