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The Kähler Rank of Compact Complex Manifolds

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Abstract

The Kähler rank was introduced by Harvey and Lawson in their 1983 paper as a measure of the kählerianity of a compact complex surface. In this work we generalize this notion to the case of compact complex manifolds and we prove several results related to this notion. We show that on class VII surfaces, there is a correspondence between the closed positive forms on a surface and those on a blow-up in a point. We also show that a manifold of maximal Kähler rank which satisfies an additional condition is in fact Kähler.

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Acknowledgments

We would like to thank Radu Alexandru Todor for his help with the proof of Proposition 3.2. Ionuţ Chiose: Supported by a Marie Curie International Reintegration Grant within the 7th European Community Framework Programme and CNCS Grant PN-II-ID-PCE-2011-3-0269.

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  1. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania

    Ionuţ Chiose

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  1. Ionuţ Chiose
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Correspondence to Ionuţ Chiose.

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Chiose, I. The Kähler Rank of Compact Complex Manifolds. J Geom Anal 26, 603–615 (2016). https://doi.org/10.1007/s12220-015-9564-z

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  • DOI: https://doi.org/10.1007/s12220-015-9564-z

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