Hipersuperfícies com Hessiano Nulo em P4

• Autor(a) principal: Freitas, Gersica Valesca Lima de
• Data de Publicação: 2013
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/9242
• topic: Hessiano; Mapa polar; GN-hipersuperfície; Franchetta hipersuperfície; Polar Map; GN-hypersurface; Franchetta hypersurface; Hessian; CIENCIAS EXATAS E DA TERRA::MATEMATICA

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].