Smooth monomial Togliatti systems of cubics

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MICHALEK, Mateusz, Rosa M. MIRÓ-ROIG, 2016. Smooth monomial Togliatti systems of cubics. In: Journal of Combinatorial Theory, Series A. Elsevier. 143, pp. 66-87. ISSN 0097-3165. eISSN 1096-0899. Available under: doi: 10.1016/j.jcta.2016.05.004

@article{Michalek2016Smoot-52340, title={Smooth monomial Togliatti systems of cubics}, year={2016}, doi={10.1016/j.jcta.2016.05.004}, volume={143}, issn={0097-3165}, journal={Journal of Combinatorial Theory, Series A}, pages={66--87}, author={Michalek, Mateusz and Miró-Roig, Rosa M.} }

2016 2021-01-11T13:23:22Z 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.<br />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. 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. Our methods rely on combinatorial properties of monomial ideals. Miró-Roig, Rosa M. Miró-Roig, Rosa M. Michalek, Mateusz Smooth monomial Togliatti systems of cubics terms-of-use eng 2021-01-11T13:23:22Z Michalek, Mateusz

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