A characterization of d-uple Veronese varieties

Abstract

Presented by Claire VoisinWe characterize d-uple Veronese embeddings of finite-dimensional projective spaces. The easiest non-trivial instance of our theorem is the embedding of the projective plane in a 5-dimensional projective space, a result obtained in 1901 by Severi when the underlying field is the field of complex numbers. © 2015 Published by Elsevier Masson SAS on behalf of Académie des sciences.r é s u m é Nous caractérisons les plongements d-uples de Veronese d'espaces projectifs de dimension finie. L'instance non triviale la plus simple de notre théorème est le plongement du plan projectif dans un espace projectif de dimension 5, un résultat obtenu en 1901 par Severi lorsque le corps sous-jacent est le corps des nombres complexes.

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 .…”