Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian
By C. Ciliberto, Francesco Russo, Aron Simis. 2007
105 citations recorded by the source corpus.
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 Jonquieres 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.
Subfields: Algebra and Number Theory, Computational Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/bee8716d85e37d32980b3247a2e4689587828ee8
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In Algebra and Number Theory
In Computational Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- On higher Hessians and the Lefschetz properties (2015, background): “1,...,Qs,u 1,...,um). 10 R.GONDIM Remark 1.27. The prove that the first s derivatives of f are algebraically dependent involves a dimensional argument. See [GN] and [Lo] for the original argument, and [CRS] for a geometric proof. Remark 1.28. All the classical constructions use the polynomial f = x 0”
- A characteristic-free criterion of birationality (2010, background): “eld degree. In addition, the Jacobian dual rank calls attention to several aspects of the theory of Rees algebras and base ideals of maps, a trend sufficiently shown in many modern accounts (see, e.g., [2], [5], [6], [7]). The paper is divided in two sections. The first section hinges on the needed bac”
- Classical Algebraic Geometry: A Modern View (2012, background): “The known cases when the assertion of Hesse is true are d = 2 (any n) and n ≤ 3 (any d) (see [254], [371], [103]).”
- Plane Cremona maps: saturation and regularity of the base ideal (2011, unknown): “, [4],[20], [21], [22], [25], [26], [27]).”
- Topics in classical algebraic geometry (2006, background): “The known cases when the assertion of Hesse is true are d = 2 (any n) and n ≤ 3 (any d) (see [138], [193], [49]).”