We introduce various families of irreducible homaloidal hypersurfaces in projective space
Pr, for all r⩾ 3. Some of these are families of homaloidal hypersurfaces whose degrees are …

Gordan and Noether proved in their fundamental theorem that an hypersurface X= V (F)⊆ P
n with n≤ 3 is a cone if and only if F has vanishing hessian (ie the determinant of the …

We deal with a generalization of a Theorem of P. Gordan and M. Noether on hypersurfaces
with vanishing (first) Hessian. We prove that for any given N≥ 3, d≥ 3 and 2≤ k< d 2 there …

We deal with Perazzo 3-folds in P 4, ie hypersurfaces X= V (f)⊂ P 4 of degree d defined by a
homogeneous polynomial f (x 0, x 1, x 2, u, v)= p 0 (u, v) x 0+ p 1 (u, v) x 1+ p 2 (u, v) x 2+ g …

We prove that for N≤ 6 an irreducible cubic hypersurface with vanishing hessian in PN is
either a cone or a scroll in linear spaces tangent to the dual of the image of the polar map of …

We introduce a new type of Hessian matrix, that we call Mixed Hessian. The mixed Hessian
is used to compute the rank of a multiplication map by a power of a linear form in a standard …

We introduce a family of Artinian Gorenstein algebras, whose combinatorial structure
characterizes the ones presented by quadrics. Under certain hypotheses these algebras …

In this paper, we study the Hessian map, which associates to any hypersurface of degree in
its Hessian hypersurface, and the general properties of this map and prove that is birational …

We deal with Perazzo hypersurfaces X= V (f) in P n+ 2 defined by a homogeneous
polynomial f (x 0, x 1,…, xn, u, v)= p 0 (u, v) x 0+ p 1 (u, v) x 1+⋯+ pn (u, v) x n+ g (u, v) …

We give a detailed proof for Gordan-Noether's results in “Ueber die algebraischen Formen,
deren Hesse'sche Determinante identisch verschwindet.” C. Lossen has written a paper in a …