Classification of Veronesean caps

Characterizations of Veronese and Segre varieties

“…Ferrara Dentice and Marino claim in [1] to have generalized the above theorem. However, they state as a fact that (Q3) implies that the tangent lines in that axiom fill a plane.…”

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

“…Such representations are called full projective embeddings. Other situations have also been investigated: lines can correspond to subsets of lines (the so-called lax projective embeddings), conics [14,18], ovals [12,20,23], ovoids [4,9,10,16] and rational normal curves [19]. For pseudo-embeddings, the lines correspond to frames of subspaces and in this case the projective space should be defined over the field F 2 .…”

Hyperplanes, parallelism, and related problems in Veronese spaces

“…The term 'Veronese space' refers, primarily (and historically), to the structure of prisms in a projective space with 'double hyperplanes' as the points (see [6,15]); after that it refers to an algebraic variety that represents this structure (cf., e.g., [1]) and as such it was generalized in recent decades and its geometry was studied and developed (see, e.g., [2,12,13,16]).…”

“…The point universe of the constructed Veronese space V k (M) consists of the k -element sets with repetitions with the elements in the universe of the underlying 'starting' structure M (cf. definitions (2) and (1)).…”