Exponential Estimate for the asymptotics of Bergman kernels

Xiaonan Ma (1) , George Marinescu (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 Mathematisches Institut

We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. We give further Bergman kernel proofs of complex geometry results, such as separation of points, existence of local coordinates and holomorphic convexity by sections of positive line bundles.

Mots clés: asymptotics of Bergman kernels; Dirac operator

Domaines: Géométrie différentielle [math.DG]; Géométrie symplectique [math.SG]; Variables complexes [math.CV]

Xiaonan Ma, George Marinescu. Exponential Estimate for the asymptotics of Bergman kernels. 2013. ⟨hal-00872450v2⟩