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

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Abstract

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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Trento, I-38050 POVO, Trento, Italy

    Lucia Alessandrini & Giovanni Bassanelli

Authors
  1. Lucia Alessandrini
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  2. Giovanni Bassanelli
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This work is partially supported by MURST, 40%.

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Alessandrini, L., Bassanelli, G. Positive\(\partial \bar \partial - closed\) currents and non-Kähler geometrycurrents and non-Kähler geometry. J Geom Anal 2, 291–316 (1992). https://doi.org/10.1007/BF02934583

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  • DOI: https://doi.org/10.1007/BF02934583

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