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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
DOI: https://doi.org/10.1090/S0002-9939-2011-10928-6
Published electronically: June 14, 2011
MathSciNet review: 2846331
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Abstract | References | Similar Articles | Additional Information

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?)

  • 1. C. Birkenhake and H. Lange, Complex Tori, Birkhäuser, 1999. MR 1713785 (2001k:14085)
  • 2. F. Campana, Twistor spaces and nonhyperbolicity of certain symplectic Kähler manifolds, Complex analysis (Wuppertal, 1991), 64-69, Aspects Math., E17, Vieweg, Braunschweig, 1991. MR 1122161 (92j:32092)
  • 3. S. Kobayashi, Hyperbolic Complex Spaces, Springer, 1998. MR 1635983 (99m:32026)
  • 4. T. Peternell, Calabi-Yau manifolds and a conjecture of Kobayashi, Math. Z. 207 (1991), 305-318. MR 1109668 (92g:14039)
  • 5. H. Royden, The Ahlfors-Schwarz lemma in several complex variables, Comment. Math. Helvetici 55 (1980), 547-558. MR 604712 (82i:32049)
  • 6. P. M. H. Wilson, Calabi-Yau manifolds with large Picard number, Invent. Math. 98 (1989), 139-155. MR 1010159 (90h:14044)
  • 7. D. Wu, S. T. Yau and F. Zheng, A degenerate Monge-Ampère equation and the boundary classes of Kähler cones, Math. Res. Lett. 16 (2009), 365-374. MR 2496750 (2010c:32061)
  • 8. S. T. Yau, A general Schwarz lemma for Kähler manifolds, Amer. J. Math. 100 (1978), 197-203. MR 0486659 (58:6370)

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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: https://doi.org/10.1090/S0002-9939-2011-10928-6
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

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