Mathematical Research Letters

Volume 17 (2010)

Number 6

On the canonical line bundle and negative holomorphic sectional curvature

Pages: 1101 – 1110

DOI: http://dx.doi.org/10.4310/MRL.2010.v17.n6.a9

Authors

Gordon Heier (Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, TX 77204, USA)

Steven S. Y. Lu (Départment de Mathématiques, Université du Qébec à Montréal, C.P. 8888, Succursale Centre-Ville, Montréal, Qc H3C 3P8, Canada)

Bun Wong (Department of Mathema)

Abstract

We prove that a smooth complex projective threefold with a Kähler metric of negative holomorphic sectional curvature has ample canonical line bundle. In dimensions greater than three, we prove that, under equal assumptions, the nef dimension of the canonical line bundle is maximal. With certain additional assumptions, ampleness is again obtained. The methods used come from both complex differential geometry and complex algebraic geometry.

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