Mathematics – Algebraic Geometry
Scientific paper
2007-01-21
Advances in Mathematics 218 (2008), 1759{1805
Mathematics
Algebraic Geometry
56 pages. Some material added in section 1; minor changes. Final version to appear in Advances in Mathematics
Scientific paper
We prove the existence of various families of irreducible homaloidal hypersurfaces in projective space $\mathbb P^ r$, for all $r\geq 3$. 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 dual hypersurfaces to certain scroll surfaces. We also introduce an infinite family of determinantal homaloidal hypersurfaces based on a certain degeneration of a generic Hankel matrix. These examples fit non--classical versions of de Jonqui\`eres 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 to the present knowledge.
Ciliberto Ciro
Russo Francesco
Simis Aron
No associations
LandOfFree
Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-516468