Hesse claimed that an irreducible projective hypersurface in $\P^n$ defined by an equation with vanishing hessian determinant is necessarily a cone. Gordan and Noether proved that this is true for n=3 and constructed counterexamples for every $n\geq 4$. Gordan and Noether and Franchetta gave classification of hypersurfaces in $\P^4$ 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.
|Titolo:||A Geometrical approach to Gordan–Noether’s and Franchetta’s contributions to a question posed by Hesse|
GARBAGNATI, ALICE (Primo)
|Parole Chiave:||Cones; Dual varieties; Vanishing hessian|
|Data di pubblicazione:||2009|
|Digital Object Identifier (DOI):||10.1007/BF03191214|
|Appare nelle tipologie:||01 - Articolo su periodico|