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Obstructions to the existence of Kähler structures on compact complex manifolds


Author: Ionuţ Chiose
Journal: Proc. Amer. Math. Soc. 142 (2014), 3561-3568
MSC (2010): Primary 32J27; Secondary 32Q15
DOI: https://doi.org/10.1090/S0002-9939-2014-12128-9
Published electronically: July 3, 2014
MathSciNet review: 3238431
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Abstract: We prove that a manifold in the Fujiki class $ {\mathcal C}$ which supports a $ i\partial \bar \partial $-closed metric is Kähler. This result implies that on a compact complex manifold in the Fujiki class $ {\mathcal C}$ which is not Kähler there exists a nonzero $ i\partial \bar \partial $-exact, positive current of bidimension $ (1,1)$.


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Additional Information

Ionuţ Chiose
Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 014700, Romania
Email: Ionut.Chiose@imar.ro

DOI: https://doi.org/10.1090/S0002-9939-2014-12128-9
Received by editor(s): November 6, 2012
Published electronically: July 3, 2014
Additional Notes: The author was supported by a Marie Curie International Reintegration Grant within the $7^{th}$ European Community Framework Programme and the CNCS grant PN-II-ID-PCE-2011-3-0269
Communicated by: Lei Ni
Article copyright: © Copyright 2014 American Mathematical Society

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