Properties of compact complex manifolds carrying closed positive currents |
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Authors: | Shanyu Ji Bernard Shiffman |
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Affiliation: | 1. Department of Mathematics, University of Houston, 77204, Houston, TX, USA 2. Department of Mathematics, The Johns Hopkins University, 21218, Baltimore, MD, USA
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Abstract: | We show that a compact complex manifold is Moishezon if and only if it carries a strictly positive, integral (1, 1)-current. We then study holomorphic line bundles carrying singular hermitian metrics with semi-positive curvature currents, and we give some cases in which these line bundles are big. We use these cases to provide sufficient conditions for a compact complex manifold to be Moishezon in terms of the existence of certain semi-positive, integral (1,1)-currents. We also show that the intersection number of two closed semi-positive currents of complementary degrees on a compact complex manifold is positive when the intersection of their singular supports is contained in a Stein domain. The first author was partially supported by National Science Foundation Grant Nos. DMS-8922760 and DMS-9204273. The second author was partially supported by National Science Foundation Grant Nos. DMS-9001365 and DMS-9204037. |
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Keywords: | KeywordHeading" >Math Subject Classification 32C30 32C40 32J20 32J25 |
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