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

Laurent Bonavero; Frédéric Campana; Jarosław A. Wiśniewski

doi:10.1016/S1631-073X(02)02284-7

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

Laurent Bonavero ¹ ; Frédéric Campana ² ; Jarosław A. Wiśniewski ³

¹ Institut Fourier, UFR de mathématiques, Université de Grenoble 1, UMR 5582, BP 74, 38402 Saint Martin d'Hères, France
² Institut Élie Cartan, Université H. Poincaré, Nancy 1, UMR 7502, BP 239, 54506 Vandoeuvre-lès-Nancy cedex, France
³ Instytut Matematyki UW Banacha 2, PL-02-097 Warszawa, Pologne

Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 463-468.

Résumé
Abstract

Nous classifions les variétés projectives complexes X pour lesquelles il existe un point a tel que l'éclatement de X en a soit une variété de Fano. Nous en déduisons qu'en dimension supérieure ou égale à trois, la quadrique est la seule variété complexe X pour laquelle il existe deux points distincts a et b tel que l'éclatement de X de centre {a,b} soit une variété 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.

Reçu le : 2002-01-21
Accepté le : 2002-01-24
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02284-7

Affiliations des auteurs :

Laurent Bonavero ¹ ; Frédéric Campana ² ; Jarosław A. Wiśniewski ³

¹ Institut Fourier, UFR de mathématiques, Université de Grenoble 1, UMR 5582, BP 74, 38402 Saint Martin d'Hères, France
² Institut Élie Cartan, Université H. Poincaré, Nancy 1, UMR 7502, BP 239, 54506 Vandoeuvre-lès-Nancy cedex, France
³ Instytut Matematyki UW Banacha 2, PL-02-097 Warszawa, Pologne

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     author = {Laurent Bonavero and Fr\'ed\'eric Campana and Jaros{\l}aw A. Wi\'sniewski},
     title = {Vari\'et\'es complexes dont l'\'eclat\'ee en un point est de {Fano}},
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Laurent Bonavero; Frédéric Campana; Jarosław A. Wiśniewski. Variétés complexes dont l'éclatée en un point est de Fano. Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 463-468. doi : 10.1016/S1631-073X(02)02284-7. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02284-7/

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