Holomorphic Line Bundles over a Tower of Coverings
- Authors
- Type
- Preprint
- Publication Date
- Oct 17, 2014
- Submission Date
- Oct 07, 2014
- Identifiers
- arXiv ID: 1410.1957
- Source
- arXiv
- License
- Yellow
- External links
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 for zero currents of random holomorphic sections. Furthermore, we obtain a variance estimate for those random zero currents, which yields the almost sure convergence under some geometric condition.