Caractérisation de l'espace projectif

Details Caractérisation de l'espace projectif Caractérisation de l'espace projectif

2003-08-22

arxiv.org/abs/math/0308212v1

Mathematics

Algebraic Geometry

12 pages, in french

Scientific paper

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 $\Omega_{X}^{1}\to L$ 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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