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, p. 719-771

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 = {Berman, Robert and Sj\"ostrand, Johannes},
     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},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 16},
     number = {4},
     year = {2007},
     pages = {719-771},
     doi = {10.5802/afst.1165},
     zbl = {pre05363338},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2007_6_16_4_719_0}
}
Berman, Robert; Sjöstrand, Johannes. 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. http://www.numdam.org/item/AFST_2007_6_16_4_719_0/

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