Nagoya Mathematical Journal

Morse inequalities for covering manifolds

Radu Todor, Ionuţ Chiose, and George Marinescu

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Abstract

We study the existence of $L^2$ holomorphic sections of invariant line bundles over Galois coverings. We show that the von Neumann dimension of the space of $L^2$ 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.

Article information

Source
Nagoya Math. J., Volume 163 (2001), 145-165.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631624

Mathematical Reviews number (MathSciNet)
MR1855193

Zentralblatt MATH identifier
1018.32022

Subjects
Primary: 32L10: Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30]
Secondary: 32F10: $q$-convexity, $q$-concavity 32Q55: Topological aspects of complex manifolds 58J37: Perturbations; asymptotics

Citation

Todor, Radu; Chiose, Ionuţ; Marinescu, George. Morse inequalities for covering manifolds. Nagoya Math. J. 163 (2001), 145--165. https://projecteuclid.org/euclid.nmj/1114631624


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