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Negative holomorphic curvature and positive canonical bundle

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Abstract

In this note we show that if a projective manifold admits a Kähler metric with negative holomorphic sectional curvature then the canonical bundle of the manifold is ample. This confirms a conjecture of the second author.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Connecticut, 196 Auditorium Road, Storrs, CT, 06269-3009, USA

    Damin Wu

  2. Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA, 02138, USA

    Shing-Tung Yau

Authors
  1. Damin Wu
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  2. Shing-Tung Yau
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Corresponding author

Correspondence to Damin Wu.

Additional information

The first author was partially supported by the NSF Grant DMS-1308837. The second author was partially supported by the NSF Grant DMS-0804454.

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Wu, D., Yau, ST. Negative holomorphic curvature and positive canonical bundle. Invent. math. 204, 595–604 (2016). https://doi.org/10.1007/s00222-015-0621-9

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  • DOI: https://doi.org/10.1007/s00222-015-0621-9

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