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The SzegÖ kernel on an orbifold circle bundle

Jian Song
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Abstract

The analysis of holomorphic sections of high powers $L^N$ of holomorphic ample line bundles $L\to M$ over compact Kähler manifolds has been widely applied in complex geometry and mathematical physics. The Tian-Yau-Zelditch's asymptotic expansion of the Szegö kernel of a circle bundle plays an important role in Kähler-Einstein geometry. We generalize the expansion for compact Kähler orbifolds with only finite isolated singularities and analyze the behavior of the expansion near the singularities.

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Jian Song. 2004-05-05. The SzegÖ kernel on an orbifold circle bundle. https://arxiv.org/abs/math/0405071

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