Constant scalar curvature kähler metrics: uniqueness, stability

Olivier Biquard

Séminaire Bourbaki (2004-2005)

  • Volume: 47, page 1-32
  • ISSN: 0303-1179

Abstract

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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.

How to cite

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Biquard, Olivier. "Métriques kählériennes à courbure scalaire constante : unicité, stabilité." Séminaire Bourbaki 47 (2004-2005): 1-32. <http://eudml.org/doc/252160>.

@article{Biquard2004-2005,
abstract = {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.},
author = {Biquard, Olivier},
journal = {Séminaire Bourbaki},
keywords = {Kähler manifold; extremal metric; stability},
language = {fre},
pages = {1-32},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {Métriques kählériennes à courbure scalaire constante : unicité, stabilité},
url = {http://eudml.org/doc/252160},
volume = {47},
year = {2004-2005},
}

TY - JOUR
AU - Biquard, Olivier
TI - Métriques kählériennes à courbure scalaire constante : unicité, stabilité
JO - Séminaire Bourbaki
PY - 2004-2005
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 47
SP - 1
EP - 32
AB - 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.
LA - fre
KW - Kähler manifold; extremal metric; stability
UR - http://eudml.org/doc/252160
ER -

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