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Smooth monomial Togliatti systems of cubics

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2016

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Miró-Roig, Rosa M.

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https://doi.org/10.1016/j.jcta.2016.05.004
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Journal of Combinatorial Theory, Series A. Elsevier. 2016, 143, pp. 66-87. ISSN 0097-3165. eISSN 1096-0899. Available under: doi: 10.1016/j.jcta.2016.05.004

Zusammenfassung

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 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.

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Fachgebiet (DDC)
510 Mathematik

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Osculating space, Weak Lefschetz property, Laplace equations, Toric threefold

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ISO 690MICHALEK, Mateusz, Rosa M. MIRÓ-ROIG, 2016. Smooth monomial Togliatti systems of cubics. In: Journal of Combinatorial Theory, Series A. Elsevier. 2016, 143, pp. 66-87. ISSN 0097-3165. eISSN 1096-0899. Available under: doi: 10.1016/j.jcta.2016.05.004
BibTex
@article{Michalek2016Smoot-52340,
  year={2016},
  doi={10.1016/j.jcta.2016.05.004},
  title={Smooth monomial Togliatti systems of cubics},
  volume={143},
  issn={0097-3165},
  journal={Journal of Combinatorial Theory, Series A},
  pages={66--87},
  author={Michalek, Mateusz and Miró-Roig, Rosa M.}
}
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