Characterizations of Veronese and Segre varieties

We survey the known and recent characterizations of Segre varieties and Veronesea varieties

A characterization of the finite Veronesean by intersection properties

A combinatorial characterization of the Veronese variety of all quadrics in PG(n, q) by means of its intersection properties with respect to subspaces is obtained. The result relies on a similar combinatorial result on the Veronesean of all conics in the plane PG(2, q) by Ferri, Hirschfeld and Thas, and Thas and Van Maldeghem, and a structural characterization of the quadric Veronesean by Thas and Van Maldeghem

On four codes with automorphism group P Sigma L(3,4) and pseudo-embeddings of the large Witt designs

A pseudo-embedding of a point-line geometry is a representation of the geometry into a projective space over the field F-2 such that every line corresponds to a frame of a subspace. Such a representation is called homogeneous if every automorphism of the geometry lifts to an automorphism of the projective space. In this paper, we determine all homogeneous pseudo-embeddings of the three Witt designs that arise by extending the projective plane PG(2, 4). Along our way, we come across some codes with automorphism group P Sigma L(3, 4) and sets of points of PG(2, 4) that have a particular intersection pattern with Baer subplanes or hyperovals

Veronesean representations of projective spaces over quadratic associative division algebras

A

Classification of finite Veronesean caps

AbstractWe show that all Veronesean caps in finite projective spaces, as defined by Mazzocca and Melone (Discrete Math. 48 (1984) 243), are projections of quadric Veroneseans. In fact we prove a slightly stronger result by weakening one of the conditions of Mazzocca and Melone