Laurent Bonavero

Variétés complexes dont l'éclatée en un point est de Fano

We classify complex projective manifolds X for which there exists a point a such that the blow-up of X at a is Fano. As a consequence, we get that, in dimension greater or equal than three, the quadric is the only complex manifold X for which there exists two distinct points a and b such that the blow-up of X with center {a,b} is Fano. To cite this article: L. Bonavero et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 463–468.

Inégalités de Morse Holomorphes Singulières

AbstractWe generalize Demailly’s holomorphic Morse inequalities to the case of a line bundle E equipped with a singular metric on an arbitrary compact complex manifold X. Our inequalities give an estimate of the cohomology groups with values in the tensor power E⊗k twisted by the corresponding sequence of multiplier ideal sheaves introduced by Nadel. The allowed singularities are of the following type: the metric is locally given by a weight exp(−φ) where

ALGEBRAIC FOLIATIONS DEFINED BY QUASI-LINES

\phi \sim \tfrac{c}{2}\log (\Sigma |f_j |^2 )

Sur une conjecture de Mukai

with holomorphic fj. As a consequence, we obtain a necessary and sufficient analytic condition, invariant by bimeromorphism, for a manifold X to be Moishezon. This characterization improves a result given by Ji and Shiffman. We finally recall and improve some results of Kollár in order to show that the corresponding sufficient conditions obtained by Siu and Demailly in the smooth case are not necessary.

On covering and quasi-unsplit families of rational curves

Given a covering family

Sur des variétés toriques non projectives

V

Factorisation faible des applications birationnelles

of effective 1-cycles on a complex projective variety

Vari\'et\'es projectives complexes dont l'\'eclat\'ee en un point est de Fano

X