The SzegÖ kernel on an orbifold circle bundle

2004/05/05 by Jian Song, Song, Jian
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.math/0405071

arxiv created 2004/05/05 · arxiv updated 2009/12/01

Abstract

The analysis of holomorphic sections of high powers L^N of holomorphic ample line bundles L→ 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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