A Geometrical approach to Gordan-Noether's and Franchetta's contributions to a question posed by Hesse

• Autores: Alice Garbagnati, Flavia Repetto
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 60, Fasc. 1, 2009, págs. 27-41
• Idioma: español
• DOI: 10.1007/bf03191214
• Enlaces
  • Texto completo
• Resumen

  • Hesse claimed in \cite{Hesse1} (and later also in \cite{Hesse2}) that an irreducible projective hypersurface in $\PP^n$ defined by an equation with vanishing hessian determinant is necessarily a cone. Gordan and Noether proved in \cite{Gordan-Noether} that this is true for $n\leq 3$ and constructed counterexamples for every $n\geq 4$. Gordan and Noether and Franchetta gave classification of hypersurfaces in $\PP^4$ with vanishing hessian and which are not cones, see \cite{{Gordan-Noether}, {Franchetta}}. Here we translate in geometric terms Gordan and Noether approach, providing direct geometrical proofs of these results

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