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.
Dans ce travail nous obtenons un développement asymptotique complet du noyau de Bergman-Hodge d’une puissance élevée d’un fibré en droites holomorphe à courbure non-dégénerée. Nous explorons aussi quelques relations avec des sections asymptotiquement holomorphes sur une variété symplectique.
@article{AFST_2007_6_16_4_719_0,
author = {Robert Berman and Johannes Sj\"ostrand},
title = {Asymptotics for {Bergman-Hodge} kernels for high powers of complex line bundles},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {719--771},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 16},
number = {4},
year = {2007},
doi = {10.5802/afst.1165},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1165/}
}
TY - JOUR AU - Robert Berman AU - Johannes Sjöstrand 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 SP - 719 EP - 771 VL - 16 IS - 4 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1165/ DO - 10.5802/afst.1165 LA - en ID - AFST_2007_6_16_4_719_0 ER -
%0 Journal Article %A Robert Berman %A Johannes Sjöstrand %T Asymptotics for Bergman-Hodge kernels for high powers of complex line bundles %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2007 %P 719-771 %V 16 %N 4 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1165/ %R 10.5802/afst.1165 %G en %F AFST_2007_6_16_4_719_0
Robert Berman; Johannes Sjöstrand. Asymptotics for Bergman-Hodge kernels for high powers of complex line bundles. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 16 (2007) no. 4, pp. 719-771. doi : 10.5802/afst.1165. https://afst.centre-mersenne.org/articles/10.5802/afst.1165/
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