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Sur une conjecture de Mukai

L. Bonavero·C. Casagrande·O. Debarre·S. Druel
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Abstract

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.

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L. Bonavero, C. Casagrande, O. Debarre, S. Druel. 2002-04-25. Sur une conjecture de Mukai. https://arxiv.org/abs/math/0204314

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