Holomorphic line bundles over a tower of coverings

Yuan Yuan, Junyan Zhu

Abstract: We study a tower of normal coverings over a compact K\"ahler manifold with holomorphic line bundles. When the line bundle is sufficiently positive, we obtain an effective estimate, which implies the Bergman stability. As a consequence, we deduce the equidistribution and almost sure convergence for zero currents of random holomorphic sections. Furthermore, we obtain a variance estimate for those random zero currents.

ArXiv: 1410.1957