It is known that the Bergman kernel associated with , 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 , 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.
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Laurent Charles 1
@article{CRMATH_2015__353_2_121_0,
author = {Laurent Charles},
title = {A note on the {Bergman} {Kernel}},
journal = {Comptes Rendus. Math\'ematique},
pages = {121--125},
publisher = {Elsevier},
volume = {353},
number = {2},
year = {2015},
doi = {10.1016/j.crma.2014.11.007},
language = {en},
}
Laurent Charles. A note on the Bergman Kernel. Comptes Rendus. Mathématique, Volume 353 (2015) no. 2, pp. 121-125. doi : 10.1016/j.crma.2014.11.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.11.007/
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