Smooth monomial Togliatti systems of cubics

dc.contributor.authorMichalek, Mateusz
dc.contributor.authorMiró-Roig, Rosa M.
dc.date.accessioned2021-01-11T13:23:22Z
dc.date.available2021-01-11T13:23:22Z
dc.date.issued2016eng
dc.description.abstractThe 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.
eng
dc.description.versionpublishedeng
dc.identifier.doi10.1016/j.jcta.2016.05.004eng
dc.identifier.urihttps://kops.uni-konstanz.de/handle/123456789/52340
dc.language.isoengeng
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dc.subjectOsculating space, Weak Lefschetz property, Laplace equations, Toric threefoldeng
dc.subject.ddc510eng
dc.titleSmooth monomial Togliatti systems of cubicseng
dc.typeJOURNAL_ARTICLEeng
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@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.}
}
kops.citation.iso690MICHALEK, 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.2016.05.004deu
kops.citation.iso690MICHALEK, 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.2016.05.004eng
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kops.sourcefieldJournal of Combinatorial Theory, Series A. Elsevier. 2016, <b>143</b>, pp. 66-87. ISSN 0097-3165. eISSN 1096-0899. Available under: doi: 10.1016/j.jcta.2016.05.004deu
kops.sourcefield.plainJournal of Combinatorial Theory, Series A. Elsevier. 2016, 143, pp. 66-87. ISSN 0097-3165. eISSN 1096-0899. Available under: doi: 10.1016/j.jcta.2016.05.004deu
kops.sourcefield.plainJournal of Combinatorial Theory, Series A. Elsevier. 2016, 143, pp. 66-87. ISSN 0097-3165. eISSN 1096-0899. Available under: doi: 10.1016/j.jcta.2016.05.004eng
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