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Bergman Kernel on Non-compact Manifolds

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Holomorphic Morse Inequalities and Bergman Kernels

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

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Abstract

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.

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(2007). Bergman Kernel on Non-compact Manifolds. In: Holomorphic Morse Inequalities and Bergman Kernels. Progress in Mathematics, vol 254. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8115-8_7

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