1,720,968 research outputs found
A characterization of the Corrado Segre variety
No full textAbstract. In this paper we give a combinatorial characterization of the Corrado Segre variety of type {n,m} in
terms of its incidence structure of points and lines
Affine Tallini sets and Grassmannians
Full text linkAbstract. In 1982/1983 A. Bichara and F. Mazzocca characterized the Grassmann space Gr(h;A)
of index h of an affine space A of dimension at least 3 over a skew-field K by means of the intersection
properties of the three disjoint families of maximal singular subspaces of Gr(h;A) and,
till now, their result represents the only known characterization of Gr(h;A). If K is a commutative
field and A has finite dimension m, then the image Gr(h;A)} under the well known Pl ̈ucker
morphism } is a proper subset Am;h;K of PG(M;K), called the affine Grassmannian
of the h-subspaces of A. The aim of this paper is to introduce the notion of Affine Tallini
Set and provide a natural and intrinsic characterization of Am;h;K from the point-line geometry
point of view. More precisely, we prove that if a projective space over a skew-field K contains an
Affine Tallini Set Δ satisfying suitable axioms on “perp” of lines, then the skew-field K is forced
to be a commutative field and Δ is an affine Grassmannian, up to projections. Furthermore, several
results concerning Affine Tallini Sets are stated and proved
- …
