The Szeg\"O kernel on an orbifold circle bundle

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