Comptes Rendus
Differential Geometry
On the asymptotic expansion of Bergman kernel
Comptes Rendus. Mathématique, Volume 339 (2004) no. 3, pp. 193-198.

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.

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.

Received:
Accepted:
Published online:
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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     title = {On the asymptotic expansion of {Bergman} kernel},
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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/

[1] N. Berline; E. Getzler; M. Vergne Heat Kernels and Dirac Operators, Springer-Verlag, 1992

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

[3] J.-M. Bismut; E. Vasserot The asymptotics of the Ray–Singer analytic torsion associated with high powers of a positive line bundle, Commun. Math. Phys., Volume 125 (1989), pp. 355-367

[4] L. Boutet de Monvel; J. Sjöstrand Sur la singularité des noyaux de Bergman et de Szegö, Astérisque, Volume 34–35 (1976), pp. 123-164

[5] D. Catlin 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

[6] X. Dai; K. Liu; X. Ma On the asymptotic expansion of Bergman kernel | arXiv

[7] S.K. Donaldson Scalar curvature and projective embeddings. I, J. Differential Geom., Volume 59 (2001) no. 3, pp. 479-522

[8] T. Kawasaki The Riemann–Roch theorem for V-manifolds, Osaka J. Math., Volume 16 (1979), pp. 151-159

[9] Z. Lu On the lower order terms of the asymptotic expansion of Tian–Yau–Zelditch, Amer. J. Math., Volume 122 (2000) no. 2, pp. 235-273

[10] X. Ma, Orbifolds and analytic torsions, Preprint

[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

[13] G. Tian On a set of polarized Kähler metrics on algebraic manifolds, J. Differential Geom., Volume 32 (1990), pp. 99-130

[14] X. Wang, Thesis, 2002

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

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