On cubic hypersurfaces with vanishing hessian

• Rodrigo Gondim ^[1] ; Francesco Russo ^[2]
  1. [1] Universidade Federal Rural de Pernambuco

     Universidade Federal Rural de Pernambuco

     Brasil

     
  2. [2] University of Catania

     University of Catania

     Catania, Italia

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 4 ((April 2015) ), 2015, págs. 779-806
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.04.030
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• Resumen

  • We prove that for N≤6N≤6 an irreducible cubic hypersurface with vanishing hessian in PNPN is either a cone or a scroll in linear spaces tangent to the dual of the image of the polar map of the hypersurface. We also provide canonical forms and a projective characterization of Special Perazzo Cubic Hypersurfaces , which, a posteriori, exhaust the class of cubic hypersurfaces with vanishing hessian, not cones, for N≤6N≤6. Finally we show by pertinent examples the technical difficulties arising for N≥7N≥7.