[L'itération de Ricci et ses applications]
Dans cette Note nous introduisons et étudions des systèmes dynamiques reliées à l'opérateur de Ricci sur l'espace des métriques kählériennes comme discrétisations des certains flots géométriques. Nous posons une conjecture concernant leurs convergence vers des métriques kählériennes canoniques and nous étudions le cas où la première classe de Chern est négative, zéro ou positive. Cette construction a plusieurs applications en géométrie kählérienne, parmi elles une réponse à une question de Nadel et une construction des faisceaux d'idéaux multiplicateurs.
In this Note we introduce and study dynamical systems related to the Ricci operator on the space of Kähler metrics as discretizations of certain geometric flows. We pose a conjecture on their convergence towards canonical Kähler metrics and study the case where the first Chern class is negative, zero or positive. This construction has several applications in Kähler geometry, among them an answer to a question of Nadel and a construction of multiplier ideal sheaves.
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@article{CRMATH_2007__345_8_445_0,
author = {Yanir A. Rubinstein},
title = {The {Ricci} iteration and its applications},
journal = {Comptes Rendus. Math\'ematique},
pages = {445--448},
publisher = {Elsevier},
volume = {345},
number = {8},
year = {2007},
doi = {10.1016/j.crma.2007.09.020},
language = {en},
}
Yanir A. Rubinstein. The Ricci iteration and its applications. Comptes Rendus. Mathématique, Volume 345 (2007) no. 8, pp. 445-448. doi : 10.1016/j.crma.2007.09.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.09.020/
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