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Comptes Rendus Mathématique
Volume 345, n° 8
pages 445-448 (octobre 2007)
Doi : 10.1016/j.crma.2007.09.020
Received : 22 June 2007 ;  accepted : 27 September 2007
The Ricci iteration and its applications
Lʼitération de Ricci et ses applications
 

Yanir A. Rubinstein
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 

Present address: Department of Mathematics, Princeton University, Princeton, NJ 08544, USA.
Abstract

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. To cite this article: Y.A. Rubinstein, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

The full text of this article is available in PDF format.
Résumé

Dans cette Note nous introduisons et étudions des systèmes dynamiques reliées à lʼopérateur de Ricci sur lʼespace 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 dʼidéaux multiplicateurs. Pour citer cet article : Y.A. Rubinstein, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

The full text of this article is available in PDF format.


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