Comptes Rendus
no. 3
Differential Geometry
On the asymptotic expansion of Bergman kernel
[Sur le développement asymptotique du noyau de Bergman.]

Présenté par : Jean-Michel Bismut

Xianzhe Dai1 ; Kefeng Liu2, 3 ; Xiaonan Ma4
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.

On étudions les développements asymptotiques du noyau de la chaleur et de Bergman de l'opérateur de Dirac spinc 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 spinc Dirac operator on high tensor powers of a line bundle.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.05.011
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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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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[11] X. Ma; G. Marinescu The spinc Dirac operator on high tensor powers of a line bundle, Math. Z., Volume 240 (2002) no. 3, pp. 651-664

[12] W. Ruan Canonical coordinates and Bergman metrics, Comm. Anal. Geom., Volume 6 (1998), pp. 589-631

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