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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Picard number, holomorphic sectional curvature, and ampleness


Authors: Pit-Mann Wong, Damin Wu and Shing-Tung Yau
Journal: Proc. Amer. Math. Soc. 140 (2012), 621-626
MSC (2010): Primary 32Q15, 32Q45, 53C55; Secondary 53C56
Published electronically: June 14, 2011
MathSciNet review: 2846331
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Abstract: We prove that for a projective manifold with Picard number equal to one, if the manifold admits a Kähler metric whose holomorphic sectional curvature is quasi-negative, then the canonical bundle of the manifold is ample.


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Additional Information

Pit-Mann Wong
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: pmwong@nd.edu

Damin Wu
Affiliation: Department of Mathematics, The Ohio State University, 1179 University Drive, Newark, Ohio 43055
Email: dwu@math.ohio-state.edu

Shing-Tung Yau
Affiliation: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138
Email: yau@math.harvard.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10928-6
PII: S 0002-9939(2011)10928-6
Received by editor(s): October 12, 2010
Received by editor(s) in revised form: November 30, 2010
Published electronically: June 14, 2011
Communicated by: Jianguo Cao
Article copyright: © Copyright 2011 American Mathematical Society