Sur une conjecture de Mukai

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Generalizing a question of Mukai, we conjecture that a Fano manifold $X$ with Picard number $ρ_X$ and pseudo-index $ι_X$ satisfies $ρ_X (ι_X-1) \le \dim(X)$. We prove this inequality in several situations: $X$ is a Fano manifold of dimension $\le 4$, $X$ is a toric Fano manifold of dimension $\le 7$ or $X$ is a toric Fano manifold of arbitrary dimension with $ι_X \ge \dim(X)/3+1$. Finally, we offer a new approach to the general case.
21 pages, in french

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Algebraic Geometry, 14J45, 14E30, 14M25

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http://salesiana.dossiersoluciones.com/handle/123456789/63915

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0204314
 http://arxiv.org/abs/math/0204314

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arXiv