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- W4221141567 abstract "Gordan and Noether proved in their fundamental theorem that an hypersurface $X=V(F)subseteq mathbb{P}^n$ with $nleq 3$ is a cone if and only if $F$ has vanishing hessian (i.e. the determinant of the Hessian matrix). They also showed that the statement is false if $ngeq 4$, by giving some counterexamples. Since their proof, several others have been proposed in the literature. In this paper we give a new one by using a different perspective which involves the study of standard Artinian Gorenstein $mathbb{K}$-algebras and the Lefschetz properties. As a further application of our setting, we prove that a standard Artinian Gorenstein algebra $R=mathbb{K}[x_0,dots,x_4]/J$ with $J$ generated by a regular sequence of quadrics has the strong Lefschetz property. In particular, this holds for Jacobian rings associated to smooth cubic threefolds." @default.
- W4221141567 created "2022-04-03" @default.
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- W4221141567 date "2022-01-19" @default.
- W4221141567 modified "2023-10-13" @default.
- W4221141567 title "A theorem of Gordan and Noether via Gorenstein rings" @default.
- W4221141567 doi "https://doi.org/10.1007/s00029-023-00882-7" @default.
- W4221141567 hasPublicationYear "2022" @default.
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