Exponential Estimate for the asymptotics of Bergman kernels

2013/10/14 by Xiaonan Ma, George Marinescu · 1 citation
Mathematics · #math.DG #math.CV #math.SG

paper · pdf · doi:10.1007/s00208-014-1137-0

published as Math. Ann. 362 (2015), no. 3-4, 1327-1347 · correct version, 15 pages

arxiv created 2013/10/14 · arxiv updated 2015/09/09

Abstract

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.

Cited by

• Tian's theorem for Grassmannian embeddings and degeneracy sets of random sections