Comptes Rendus
no. 7
Differential Geometry
Generalized Bergman kernels on symplectic manifolds
[Noyaux de Bergman généralisés sur les variétés symplectiques.]

Présenté par : Jean-Michel Bismut

Xiaonan Ma1 ; George Marinescu2 
1 Centre de mathématiques, UMR 7640 du CNRS, École polytechnique, 91128 Palaiseau cedex, France
2 Humboldt-Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, 12489 Berlin, Germany
Comptes Rendus. Mathématique, Volume 339 (2004) no. 7, pp. 493-498.

On étudie le développement asymptotique du noyau de Bergman généralisé du Laplacien de Bochner renormalisé associé à une puissance tendant vers l'infini d'un fibré en droites positif sur une variété symplectique compacte.

We study the asymptotic of the generalized Bergman kernels of the renormalized Bochner–Laplacian on high tensor powers of a positive line bundle on compact symplectic manifolds.

Reçu le :
Publié le :
DOI : 10.1016/j.crma.2004.07.016
Xiaonan Ma 1 ; George Marinescu 2

1 Centre de mathématiques, UMR 7640 du CNRS, École polytechnique, 91128 Palaiseau cedex, France
2 Humboldt-Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, 12489 Berlin, Germany 
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Xiaonan Ma; George Marinescu. Generalized Bergman kernels on symplectic manifolds. Comptes Rendus. Mathématique, Volume 339 (2004) no. 7, pp. 493-498. doi : 10.1016/j.crma.2004.07.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.07.016/

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[4] X. Dai; K. Liu; X. Ma On the asymptotic expansion of Bergman kernel, C. R. Acad. Sci. Paris, Ser. I, Volume 339 (2004), pp. 193-198 (The full version:) | arXiv

[5] V. Guillemin; A. Uribe The Laplace operator on the nth tensor power of a line bundle: eigenvalues which are bounded uniformly in n, Asymptotic Anal., Volume 1 (1988), pp. 105-113

[6] Z. Lu On the lower order terms of the asymptotic expansion of Tian–Yau–Zelditch, Am. J. Math., Volume 122 (2000), pp. 235-273

[7] X. Ma; G. Marinescu The spinc Dirac operator on high tensor powers of a line bundle, Math. Z., Volume 240 (2002), pp. 651-664

[8] X. Ma, G. Marinescu, Generalized Bergman kernels on symplectic manifolds, Preprint

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