Properties of compact complex manifolds carrying closed positive currents

  • Shanyu Ji
  • Bernard Shiffman
Article

DOI: 10.1007/BF02921329

Cite this article as:
Ji, S. & Shiffman, B. J Geom Anal (1993) 3: 37. doi:10.1007/BF02921329

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.

Math Subject Classification

32C30 32C40 32J20 32J25 

Key Words and Phrases

Chern class compact complex manifold singular hermitian metric holomorphic line bundle Iitaka dimension intersection number Kähler current Lelong number Moishezon manifold positive current Stein manifold 

Copyright information

© Mathematica Josephina, Inc. 1993

Authors and Affiliations

  • Shanyu Ji
    • 1
    • 2
  • Bernard Shiffman
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Department of MathematicsThe Johns Hopkins UniversityBaltimoreUSA

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