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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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


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:
  • Damin Wu
  • Affiliation: Department of Mathematics, The Ohio State University, 1179 University Drive, Newark, Ohio 43055
  • MR Author ID: 799841
  • Email:
  • 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:
  • 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:
  • MathSciNet review: 2846331