Limit of Bergman kernels on a tower of coverings of compact Kähler manifolds

Abstract

We prove the convergence of the Bergman kernels and the L2-Hodge numbers on a tower of Galois coverings { Xj} of a compact Kähler manifold X converging to an infinite Galois (not necessarily universal) covering X~. We also show that, as an application, sections of canonical line bundle KXj for sufficiently large j give rise to an immersion into some projective space, if so do sections of KX~. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.