In this paper we classify all Veronesean caps of projective spaces of finite dimension over skew-fields. More precisely, we prove that if the projective space PG(M,K), K a skew-field, contains a Veronesean cap X, then K is a field and X is either a Veronese variety or a projection of a Veronese variety. This result extends analogous theorems of Mazzocca and Melone and Thas and Van Maldeghem for finite projective spaces.
Classification of Veronesean caps
FERRARA DENTICE, Eva;MARINO, Giuseppe
2008
Abstract
In this paper we classify all Veronesean caps of projective spaces of finite dimension over skew-fields. More precisely, we prove that if the projective space PG(M,K), K a skew-field, contains a Veronesean cap X, then K is a field and X is either a Veronese variety or a projection of a Veronese variety. This result extends analogous theorems of Mazzocca and Melone and Thas and Van Maldeghem for finite projective spaces.File in questo prodotto:
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