Une nouvelle caractérisation des variétés de Veronese

Details Une nouvelle caractérisation des variétés de Veronese Une nouvelle caractérisation des variétés de Veronese

2010-12-05

arxiv.org/abs/1012.1008v1

Mathematics

Algebraic Geometry

13 pages

Scientific paper

Let $X$ be the germ of a smooth complex variety at a given point $x\in {\mathbbb P}^N$ with regular osculation at order $q$ and suppose that, for any direction $v\in {\mathbbb P}T_xX$, there exists a rationnal normal curve locally contained in $X$ and passing through the point $x$ in direction $v$. We show that $X$ is necessarily a Veronese variety of order $q$. As a special case, we recover a classical result of Bompiani, in which it is assumed that the condition is verified by any point close to $x$.

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