Corrado Zanella

On embeddings of minimum dimension of PG(n,q) × PG(n,q)

A construction is given of an embedding of \({\mathrm{PG}}(n-1,q)\times {\mathrm{PG}}(n-1,q)\) into \({\mathrm{PG}}(2n-1,q)\), i.e. of minimum dimension, and it is shown that the image is a nonsingular hypersurface of degree \(n\). The construction arises from a scattered subspace with respect to a Desarguesian spread in \({\mathrm{PG}}(2n-1,q)\). By construction there are two systems of maximum subspaces (in this case \((n-1)\)-dimensional) which cover this hypersurface. However, unlike the standard Segre embedding, the minimum embedding constructed here allows another \(n-2\) systems of maximum subspaces which cover this embedding. We describe these systems and study the stabiliser of these embeddings. The results can be considered as a generalization of the properties of the hyperbolic quadric \(Q^+(3,q)\).

Embeddings of Grassmann spaces

AbstractIn this paper we show a construction, inductive onn, of the Grassmannian

Linear Sections of the Finite Veronese Varieties and AuthenticationSystems Defined Using Geometry

\mathcal{G}_{n,1,F}

On embeddings of minimum dimension of {\mathrm{PG}}(n,q)\times {\mathrm{PG}}(n,q)

representing the lines of the projective spacePn,F:

On the order structure in the line geometry of a projective space

\mathcal{G}_{n,1,F}

Topological affine spaces

is the union of those planes, any of which is obtained by joining a line of a certain (n−1)-flat Sn−1 with the corresponding point on