Geodesic
Complex analysis/Differential geometry
A note on the Bergman Kernel
[Sur le noyau de Bergman]

Présenté par : Jean-Pierre Demailly

Charles, Laurent1
1 Institut de mathématiques de Jussieu-Paris rive gauche, 4, place Jussieu, 75252 Paris, France
Comptes Rendus. Mathématique, Tome 353 (2015) no. 2, pp. 121-125.

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It is known that the Bergman kernel associated with Lk, where L is positive line bundle over a complex compact manifold, has an asymptotic expansion. We give an elementary proof of the fact that the subprincipal term of this expansion is the scalar curvature.

Il est connu que le noyau de Bergman associé à Lk, où L est un fibré en droite positif sur une variété complexe compacte, admet un développement asymptotique. Nous prouvons de manière élémentaire que le terme sous-principal de ce développement est donné par la courbure scalaire.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.11.007

Charles, Laurent 1

1 Institut de mathématiques de Jussieu-Paris rive gauche, 4, place Jussieu, 75252 Paris, France 
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Charles, Laurent. A note on the Bergman Kernel. Comptes Rendus. Mathématique, Tome 353 (2015) no. 2, pp. 121-125. doi : 10.1016/j.crma.2014.11.007. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2014.11.007/

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