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Morse inequalities for covering manifolds

Published online by Cambridge University Press:  22 January 2016

Radu Todor ,
Ionuţ Chiose  and
George Marinescu
Radu Todor
Affiliation:
Faculty of Mathematics, University of Bucharest, Str Academiei 14, Bucharest, Romania
Ionuţ Chiose
Affiliation:
Department of Mathematics, SUNY at Stony Brook, Stony Brook, NY 11794-3651, USAchiose@math.sunysb.edu
George Marinescu*
Affiliation:
Institute of Mathematics of the Romanian Academy, Bucharest, Romania
*
Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Deutschlandgeorge@mathematik.hu-berlin.de
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Abstract

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We study the existence of L2 holomorphic sections of invariant line bundles over Galois coverings. We show that the von Neumann dimension of the space of L2 holomorphic sections is bounded below under weak curvature conditions. We also give criteria for a compact complex space with isolated singularities and some related strongly pseudoconcave manifolds to be Moishezon. As applications we prove the stability of the previous Moishezon pseudoconcave manifolds under perturbation of complex structures as well as weak Lefschetz theorems.

Keywords

58J3732F1032Q55
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 163 , September 2001 , pp. 145 - 165
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

Footnotes

1

Supported by a DFG Stipendium at the Graduiertenkolleg ‘Geometrie und Nichtlineare Analysis’ at Humboldt-Universität zu Berlin and SFB 288.

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