Journal of Differential Geometry

Kähler manifolds of semi-negative holomorphic sectional curvature

Gordon Heier, Steven S. Y. Lu, and Bun Wong

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In an earlier work, we investigated some consequences of the existence of a Kähler metric of negative holomorphic sectional curvature on a projective manifold. In the present work, we extend our results to the case of semi-negative (i.e., non-positive) holomorphic sectional curvature. In doing so, we define a new invariant that records the largest codimension of maximal subspaces in the tangent spaces on which the holomorphic sectional curvature vanishes. Using this invariant, we establish lower bounds for the nef dimension and, under certain additional assumptions, for the Kodaira dimension of the manifold. In dimension two, a precise structure theorem is obtained.

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J. Differential Geom., Volume 104, Number 3 (2016), 419-441.

Received: 15 March 2014
First available in Project Euclid: 3 November 2016

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Heier, Gordon; Lu, Steven S. Y.; Wong, Bun. Kähler manifolds of semi-negative holomorphic sectional curvature. J. Differential Geom. 104 (2016), no. 3, 419--441. doi:10.4310/jdg/1478138548.

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