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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.

References [Enhancements On Off] (What's this?)

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Additional Information

Pit-Mann Wong
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

Damin Wu
Affiliation: Department of Mathematics, The Ohio State University, 1179 University Drive, Newark, Ohio 43055

Shing-Tung Yau
Affiliation: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138

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

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