Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian
-
Autores: Ciro Ciliberto
, Francesco Russo , Aron Simis
- Localización: Advances in mathematics, ISSN 0001-8708, Vol. 218, Nº 6, 2008, págs. 1759-1805
- Idioma: inglés
- DOI: 10.1016/j.aim.2008.03.025
- Texto completo no disponible (Saber más ...)
-
Resumen
We introduce various families of irreducible homaloidal hypersurfaces in projective space , for all r3. Some of these are families of homaloidal hypersurfaces whose degrees are arbitrarily large as compared to the dimension of the ambient projective space. The existence of such a family solves a question that has naturally arisen from the consideration of the classes of homaloidal hypersurfaces known so far. The result relies on a fine analysis of hypersurfaces that are dual to certain scroll surfaces. We also introduce an infinite family of determinantal homaloidal hypersurfaces based on a certain degeneration of a generic Hankel matrix. The latter family fit non-classical versions of de Jonquières transformations. As a natural counterpoint, we broaden up aspects of the theory of Gordan�Noether hypersurfaces with vanishing Hessian determinant, bringing over some more precision into the present knowledge.
