no. 6
Algebraic Geometry/Differential Geometry
Kähler manifolds with numerically effective Ricci class and maximal first Betti number are tori
[Les variétés kählériennes de classe de Ricci numériquement effective et de premier nombre de Betti maximal sont les tores]

Présenté par : Jean-Pierre Demailly

Fang, Fuquan1, 2
1 Department of Mathematics, Capital Normal University, Beijing 100037, PR China
2 Chern Institute of Mathematics, Nankai University, Tianjin 300071, PR China
Comptes Rendus. Mathématique, Tome 342 (2006) no. 6, pp. 411-416.

Soit M une variété kählérienne compacte de dimension n et de classe de Ricci c1(M) numériquement effective. Dans cette note nous montrons que si le premier nombre de Betti b1(M) est égal à 2n, alors M est biholomorphe à un tore complexe de dimension n.

Let M be a n-dimensional Kähler manifold with numerically effective Ricci class c1(M). In this Note we prove that, if the first Betti number b1(M) is equal to 2n, then M is biholomorphic to a n-dimensional complex torus.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.11.019
Fang, Fuquan 1, 2

1 Department of Mathematics, Capital Normal University, Beijing 100037, PR China
2 Chern Institute of Mathematics, Nankai University, Tianjin 300071, PR China 
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Fang, Fuquan. Kähler manifolds with numerically effective Ricci class and maximal first Betti number are tori. Comptes Rendus. Mathématique, Tome 342 (2006) no. 6, pp. 411-416. doi : 10.1016/j.crma.2005.11.019. http://www.numdam.org/articles/10.1016/j.crma.2005.11.019/

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