Asymptotics for Bergman-Hodge kernels for high powers of complex line bundles

Robert Berman[1]; Johannes Sjöstrand[2]

  • [1] Department of Mathematics, Chalmers University of Technology, Eklandag. 86, SE-412 96 Göteborg
  • [2] CMLS, Ecole Polytechnique, FR-91128 Palaiseau cedex, UMR 7640, CNRS.

Annales de la faculté des sciences de Toulouse Mathématiques (2007)

  • Volume: 16, Issue: 4, page 719-771
  • ISSN: 0240-2963

Abstract

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In this paper we obtain the full asymptotic expansion of the Bergman-Hodge kernel associated to a high power of a holomorphic line bundle with non-degenerate curvature. We also explore some relations with asymptotic holomorphic sections on symplectic manifolds.

How to cite

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Berman, Robert, and Sjöstrand, Johannes. "Asymptotics for Bergman-Hodge kernels for high powers of complex line bundles." Annales de la faculté des sciences de Toulouse Mathématiques 16.4 (2007): 719-771. <http://eudml.org/doc/10068>.

@article{Berman2007,
abstract = {In this paper we obtain the full asymptotic expansion of the Bergman-Hodge kernel associated to a high power of a holomorphic line bundle with non-degenerate curvature. We also explore some relations with asymptotic holomorphic sections on symplectic manifolds.},
affiliation = {Department of Mathematics, Chalmers University of Technology, Eklandag. 86, SE-412 96 Göteborg; CMLS, Ecole Polytechnique, FR-91128 Palaiseau cedex, UMR 7640, CNRS.},
author = {Berman, Robert, Sjöstrand, Johannes},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Bergman kernel; Dolbeault cohomology group},
language = {eng},
number = {4},
pages = {719-771},
publisher = {Université Paul Sabatier, Toulouse},
title = {Asymptotics for Bergman-Hodge kernels for high powers of complex line bundles},
url = {http://eudml.org/doc/10068},
volume = {16},
year = {2007},
}

TY - JOUR
AU - Berman, Robert
AU - Sjöstrand, Johannes
TI - Asymptotics for Bergman-Hodge kernels for high powers of complex line bundles
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2007
PB - Université Paul Sabatier, Toulouse
VL - 16
IS - 4
SP - 719
EP - 771
AB - In this paper we obtain the full asymptotic expansion of the Bergman-Hodge kernel associated to a high power of a holomorphic line bundle with non-degenerate curvature. We also explore some relations with asymptotic holomorphic sections on symplectic manifolds.
LA - eng
KW - Bergman kernel; Dolbeault cohomology group
UR - http://eudml.org/doc/10068
ER -

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