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

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dc.creatorGarbagnati, Alice
dc.creatorRepetto, Flavia
dc.date2008-02-07
dc.date.accessioned2026-07-07T09:19:15Z
dc.date.available2026-07-07T09:19:15Z
dc.descriptionHesse claimed that an irreducible projective hypersurface in $\PP^n$ defined by an equation with vanishing hessian determinant is necessarily a cone. Gordan and Noether proved 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. Here we translate in geometric terms Gordan and Noether approach, providing direct geometrical proofs of these results.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/0802.0959
dc.identifierhttp://arxiv.org/abs/0802.0959
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154323
dc.subjectAlgebraic Geometry
dc.subject14J70
dc.titleA geometrical approach to Gordan--Noether's and Franchetta's contributions to a question posed by Hesse
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