L^2RiemannRoch Inequalities for Covering Manifolds
Abstract
We study the existence of $L^2$ holomorphic sections of invariant line bundles over Galois coverings of Zariski open sets in Moishezon manilolds. We show that the von Neuman dimension of the space of $L^2$ holomorphic sections is bounded below under reasonable curvature conditions. We also give criteria for a a compact complex space with isolated singularities and some related strongly pseudoconcave manifolds to be Moishezon. Their coverings are then studied with the same methods. As applications we give weak Lefschetz theorems using the NapierRamachandran proof of the Nori theorem.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2000
 arXiv:
 arXiv:math/0002049
 Bibcode:
 2000math......2049T
 Keywords:

 Algebraic Geometry;
 32J20
 EPrint:
 AMStex, 27 pages