Bergman Kernel on Non-compact Manifolds

Part of the Progress in Mathematics book series (PM, volume 254)


We show in Section 6.1 that the asymptotic expansion of the Bergman kernel still holds on compact sets of certain non-compact complete manifolds. In this way we can obtain another proof of some of the holomorphic Morse inequalities. As a corollary, we re-prove the Shiffman-Ji-Bonavero-Takayama criterion for Moishezon manifolds in Section 6.2.


Line Bundle Complex Manifold Ahler Manifold Pseudoconvex Domain Bergman Kernel 
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