Bergman kernels and symplectic reduction

Xiaonan Ma; Weiping Zhang

doi:10.1016/j.crma.2005.07.009

Differential Geometry

Bergman kernels and symplectic reduction

Presented by: Jean-Michel Bismut

Xiaonan Ma ¹; Weiping Zhang ²

¹ Centre de mathématiques, UMR 7640 du CNRS, École polytechnique, 91128 Palaiseau cedex, France
² Nankai Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, PR China

Comptes Rendus. Mathématique, Volume 341 (2005) no. 5, pp. 297-302.

Abstract
Résumé

We present several results concerning the asymptotic expansion of the invariant Bergman kernel of the ${spin}^{c}$ Dirac operator associated with high tensor powers of a positive line bundle on a compact symplectic manifold.

Nous annonçons des résultats sur le développement asymptotique du noyau de Bergman G-invariant de l'opérateur de Dirac ${spin}^{c}$ associé à une puissance tendant vers l'infini d'un fibré en droites positif sur une variété symplectique compacte.

Received: 2005-07-09
Accepted: 2005-07-18
Published online: 2005-08-24

DOI: 10.1016/j.crma.2005.07.009

Author's affiliations:

Xiaonan Ma ¹; Weiping Zhang ²

¹ Centre de mathématiques, UMR 7640 du CNRS, École polytechnique, 91128 Palaiseau cedex, France
² Nankai Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, PR China

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     author = {Xiaonan Ma and Weiping Zhang},
     title = {Bergman kernels and symplectic reduction},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {297--302},
     publisher = {Elsevier},
     volume = {341},
     number = {5},
     year = {2005},
     doi = {10.1016/j.crma.2005.07.009},
     language = {en},
}

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Xiaonan Ma; Weiping Zhang. Bergman kernels and symplectic reduction. Comptes Rendus. Mathématique, Volume 341 (2005) no. 5, pp. 297-302. doi : 10.1016/j.crma.2005.07.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.07.009/

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Cited by

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