[Sur le noyau de Bergman]
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.
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.
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@article{CRMATH_2015__353_2_121_0,
author = {Charles, Laurent},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.11.007/}
}
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://www.numdam.org/articles/10.1016/j.crma.2014.11.007/
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