Positive\(\partial \bar \partial - closed\) currents and non-Kähler geometrycurrents and non-Kähler geometry

  • Lucia Alessandrini
  • Giovanni Bassanelli


In this paper some new results on positive\(\partial \bar \partial - closed\) currents are applied to modifications\(f:\bar M \to M\). The main result in this topic is that every smooth proper modification of a compact Kähler manifoldM is balanced. Moreover, under suitable hypotheses on the map, the Kähler degrees of\(\bar M\) corresponds to homological properties of the exceptional set of the modification. More examples ofp-Kähler manifolds are discussed in the last section of the paper.

Math Subject Classification

Primary 32C30, 53C65 Secondary 32C10, 32J27 

Key Words and Phrases

Kähler and balanced manifolds modifications positive currents 


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Copyright information

© Mathematica Josephina, Inc. 1992

Authors and Affiliations

  • Lucia Alessandrini
    • 1
  • Giovanni Bassanelli
    • 1
  1. 1.Dipartimento di MatematicaUniversità di TrentoTrentoItaly

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