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arXiv · 1410.1957

Holomorphic Line Bundles over a Tower of Coverings

Yuan Yuan·Junyan Zhu
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Abstract

We study a tower of normal coverings over a compact Kähler 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.

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Yuan Yuan, Junyan Zhu. 2014-10-18. Holomorphic Line Bundles over a Tower of Coverings. https://arxiv.org/abs/1410.1957

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