Picard number, holomorphic sectional curvature, and ampleness
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- by Pit-Mann Wong, Damin Wu and Shing-Tung Yau PDF
- Proc. Amer. Math. Soc. 140 (2012), 621-626 Request permission
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
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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
- MR Author ID: 799841
- Email: dwu@math.ohio-state.edu
- Shing-Tung Yau
- Affiliation: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138
- MR Author ID: 185480
- ORCID: 0000-0003-3394-2187
- Email: yau@math.harvard.edu
- 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
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 621-626
- MSC (2010): Primary 32Q15, 32Q45, 53C55; Secondary 53C56
- DOI: https://doi.org/10.1090/S0002-9939-2011-10928-6
- MathSciNet review: 2846331