We compute the Szego kernel of the unit circle bundle of a negative line bundle dual to a regular quantum line bundle over a compact Kahler manifold. As a corollary we provide an infinite family of smoothly bounded strictly pseudoconvex domains on complex manifolds (disk bundles over homogeneous Hodge manifolds) for which the log-terms in the Fefferman expansion of the Szego kernel vanish and which are not locally CR-equivalent to the sphere. We also give a proof of the fact that, for homogeneous Hodge manifolds, the existence of a locally spherical CR-structure on the unit circle bundle alone implies that the manifold is biholomorphic to a projective space. Our results generalize those obtained by M. Engliˇs and G. Zhang for Hermitian symmetric spaces of compact type.

Szegö kernel, regular quantizations and spherical CR-structures / Arezzo, Claudio; A., Loi; F., Zuddas. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 275:3-4(2013), pp. 1207-1216. [10.1007/s00209-013-1178-1]

Szegö kernel, regular quantizations and spherical CR-structures.

AREZZO, Claudio;
2013-01-01

Abstract

We compute the Szego kernel of the unit circle bundle of a negative line bundle dual to a regular quantum line bundle over a compact Kahler manifold. As a corollary we provide an infinite family of smoothly bounded strictly pseudoconvex domains on complex manifolds (disk bundles over homogeneous Hodge manifolds) for which the log-terms in the Fefferman expansion of the Szego kernel vanish and which are not locally CR-equivalent to the sphere. We also give a proof of the fact that, for homogeneous Hodge manifolds, the existence of a locally spherical CR-structure on the unit circle bundle alone implies that the manifold is biholomorphic to a projective space. Our results generalize those obtained by M. Engliˇs and G. Zhang for Hermitian symmetric spaces of compact type.
2013
Szegö kernel, regular quantizations and spherical CR-structures / Arezzo, Claudio; A., Loi; F., Zuddas. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 275:3-4(2013), pp. 1207-1216. [10.1007/s00209-013-1178-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2673227
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