Métriques kählériennes à courbure scalaire constante : unicité, stabilité

Biquard, Olivier

Séminaire Bourbaki : volume 2004/2005, exposés 938-951, Astérisque, no. 307 (2006), Exposé no. 938, pp. 1-31.

Un des problèmes les plus intéressants de la géométrie différentielle complexe consiste à comprendre les classes de Kähler de variétés complexes admettant des métriques à courbure scalaire constante. La question de l'unicité a été récemment résolue par Donaldson, Mabuchi, Chen-Tian. Des liens forts avec la stabilité algébrique des variétés ont été mis en évidence. L'exposé s'attachera à exposer les idées nouvelles qui ont mené à ces résultats.

One of the most interesting problems in complex differential geometry is to understand the Kähler classes of complex compact manifolds which admit constant scalar curvature metrics. The uniqueness question has been recently solved in the works of Donaldson, Mabuchi, Chen and Tian, and strong relations appeared between existence and the stability of algebraic varieties. The seminar explains some of the new ideas leading to these results.

Classification : 32Q15, 53D20, 53C55
Mot clés : variété kählérienne, métrique extrémale, stabilité
Keywords: Kähler manifold, extremal metric, stability

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