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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Abstract

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1478138548

Digital Object Identifier
doi:10.4310/jdg/1478138548

Mathematical Reviews number (MathSciNet)
MR3568627

Zentralblatt MATH identifier
06673635

Citation

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. https://projecteuclid.org/euclid.jdg/1478138548


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