Hipersuperfícies com Hessiano Nulo em P4

Abstract

Hesse claimed in [9] that an irreducible projective hypersurface in Pn de ned by an equation with vanishing hessian determinant is necessarily a cone. Gordan and Noether proved in [6] that this is true for n 3 and constructed counterexamples for every n 4. Gordan-Noether and Franchetta gave a classi cation of hypersurfaces in P4 with vanishing hessian and which are not cones, see [6] and [3]. Here we give a geometric approach to the classi cation proposed by Gordan-Noether, providing a classi cation of hypersurfaces with zero Hessian in P4, following the lines of Garbagnati-Reppeto in [4].