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 Engli (Math Z 264(4):901-912, 2010) for Hermitian symmetric spaces of compact type.
Szego kernel, regular quantizations and spherical CR-structures
LOI, ANDREA;ZUDDAS, FABIO
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 Engli (Math Z 264(4):901-912, 2010) for Hermitian symmetric spaces of compact type.File | Dimensione | Formato | |
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