no. 7
Differential Geometry
Generalized Bergman kernels on symplectic manifolds
[Noyaux de Bergman généralisés sur les variétés symplectiques.]
Présenté par : Jean-Michel Bismut
Ma, Xiaonan1 ; Marinescu, George2 
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, Tome 339 (2004) no. 7, pp. 493-498

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.

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.

Reçu le :
Publié le :
DOI : 10.1016/j.crma.2004.07.016

Ma, Xiaonan 1 ; Marinescu, George 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 
@article{CRMATH_2004__339_7_493_0,
     author = {Ma, Xiaonan and Marinescu, George},
     title = {Generalized {Bergman} kernels on symplectic manifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {493--498},
     year = {2004},
     publisher = {Elsevier},
     volume = {339},
     number = {7},
     doi = {10.1016/j.crma.2004.07.016},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.crma.2004.07.016/}
}
TY  - JOUR
AU  - Ma, Xiaonan
AU  - Marinescu, George
TI  - Generalized Bergman kernels on symplectic manifolds
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 493
EP  - 498
VL  - 339
IS  - 7
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.crma.2004.07.016/
DO  - 10.1016/j.crma.2004.07.016
LA  - en
ID  - CRMATH_2004__339_7_493_0
ER  - 
%0 Journal Article
%A Ma, Xiaonan
%A Marinescu, George
%T Generalized Bergman kernels on symplectic manifolds
%J Comptes Rendus. Mathématique
%D 2004
%P 493-498
%V 339
%N 7
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.crma.2004.07.016/
%R 10.1016/j.crma.2004.07.016
%G en
%F CRMATH_2004__339_7_493_0
Ma, Xiaonan; Marinescu, George. Generalized Bergman kernels on symplectic manifolds. Comptes Rendus. Mathématique, Tome 339 (2004) no. 7, pp. 493-498. doi: 10.1016/j.crma.2004.07.016

[1] Bismut, J.-M.; Lebeau, G. Complex immersions and Quillen metrics, Publ. Math. IHES, Volume 74 (1991), pp. 1-297

[2] Borthwick, D.; Uribe, A. The spectral density function for the Laplacian on high tensor powers of a line bundle, Ann. Global Anal. Geom., Volume 21 (2002), pp. 269-286

[3] Catlin, D. The Bergman kernel and a theorem of Tian. Analysis and geometry in several complex variables (Katata, 1997), Trends Math., Birkhäuser Boston, Boston, MA, 1999, pp. 1-23

[4] Dai, X.; Liu, K.; Ma, X. 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] Guillemin, V.; Uribe, A. 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] Lu, Z. On the lower order terms of the asymptotic expansion of Tian–Yau–Zelditch, Am. J. Math., Volume 122 (2000), pp. 235-273

[7] Ma, X.; Marinescu, G. 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

[9] X. Wang, Thesis, 2002

[10] Zelditch, S. Szegö kernels and a theorem of Tian, Internat. Math. Res. Notices, Volume 6 (1998), pp. 317-331

Cité par Sources :