On the asymptotic expansion of Bergman kernel

Xianzhe Dai; Kefeng Liu; Xiaonan Ma

doi:10.1016/j.crma.2004.05.011

Differential Geometry

On the asymptotic expansion of Bergman kernel
[Sur le développement asymptotique du noyau de Bergman.]

Présenté par : Jean-Michel Bismut

Xianzhe Dai ¹ ; Kefeng Liu ^2,³ ; Xiaonan Ma ⁴

¹ Department of Mathematics, UCSB, California, CA 93106, USA
² Center of Mathematical Science, Zhejiang University, China
³ Department of Mathematics, UCLA, California, CA 90095-1555, USA
⁴ Centre de mathématiques, CNRS UMR 7640, École polytechnique, 91128 Palaiseau cedex, France

Comptes Rendus. Mathématique, Volume 339 (2004) no. 3, pp. 193-198.

Résumé
Abstract

On étudions les développements asymptotiques du noyau de la chaleur et de Bergman de l'opérateur de Dirac ${spin}^{c}$ associé à une puissance grande d'un fibré en droites positif.

We study the asymptotics of the Bergman kernel and the heat kernel of the ${spin}^{c}$ Dirac operator on high tensor powers of a line bundle.

Reçu le : 2004-05-14
Accepté le : 2004-05-18
Publié le : 2004-07-23

DOI : 10.1016/j.crma.2004.05.011

Affiliations des auteurs :

Xianzhe Dai ¹ ; Kefeng Liu ^{2, 3} ; Xiaonan Ma ⁴

¹ Department of Mathematics, UCSB, California, CA 93106, USA
² Center of Mathematical Science, Zhejiang University, China
³ Department of Mathematics, UCLA, California, CA 90095-1555, USA
⁴ Centre de mathématiques, CNRS UMR 7640, École polytechnique, 91128 Palaiseau cedex, France

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     author = {Xianzhe Dai and Kefeng Liu and Xiaonan Ma},
     title = {On the asymptotic expansion of {Bergman} kernel},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {193--198},
     publisher = {Elsevier},
     volume = {339},
     number = {3},
     year = {2004},
     doi = {10.1016/j.crma.2004.05.011},
     language = {en},
}

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Xianzhe Dai; Kefeng Liu; Xiaonan Ma. On the asymptotic expansion of Bergman kernel. Comptes Rendus. Mathématique, Volume 339 (2004) no. 3, pp. 193-198. doi : 10.1016/j.crma.2004.05.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.05.011/

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