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L. Bonavero

Publications and source records attributed to L. Bonavero.

5 recordsLinked to original sources
arXiv2010

Variétés rationnellement connexes sur un corps algébriquement clos

These are lectures notes on rationally connected varieties, written for the "Etats de la Recherche" of the French Mathematical Society held in Strasbourg (May 2008). We focus on geometric aspects. These notes have been written in order that a wide audience can easily read them, except maybe the last section, a bit more technical, where we give the proof of Shokurov rational connectedness conjecture following Hacon and McKernan. ----- Ce sont les notes d'un mini-cours sur les variétés rationnellement connexes, écrit pour les Etats de la Recherche de la Société Mathématique de France (Strasbourg, 2008). On met l'accent sur les aspects géométriques. Ce cours est rédigé dans l'espoir de s'adresser à un public large, à l'exception peut-être du §7, où nous donnons les grandes lignes de la preuve de la conjecture de connexité rationnelle de Shokurov par Hacon et McKernan, plus technique et où les prérequis sont un peu plus importants.

math.AG↗
arXiv2005

On covering and quasi-unsplit families of rational curves

We study extremality properties of covering families of rational curves on projective varieties. Among others, we show that on a normal and Q-factorial projective variety of dimension at most 4, every covering and quasi-unsplit family of rational curves generates a geometric extremal ray of the Mori cone.

math.AG↗
arXiv2002

Sur une conjecture de Mukai

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.

math.AG↗