arXiv math/03082122003-08-22math.AG

Caractérisation de l'espace projectif

Stéphane Druel

备注：: 12 pages, in french

英文摘要：

The purpose of this paper is to prove the following theorem. Let $X$ be a projective normal variety defined over an algebraically closed field of characteristic zero and let $Ω_{X}^{1}\to L$ be a one-dimensional foliation on $X$. If $L\cdot C<0$ for all curves $C\subset X$ then either the foliation is regular or else $X$ is a cone over a normal projective variety. This strengthens Wahl's well-known cohomological characterization of the projective space and gives a geometric proof of his results.

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