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Towards a Mori theory on compact Kähler threefolds III

Thomas Peternell — 2001

Bulletin de la Société Mathématique de France

Based on the results of the first two parts to this paper, we prove that the canonical bundle of a minimal Kähler threefold ( K X is nef) is good,its Kodaira dimension equals the numerical Kodaira dimension, (in particular some multiple of K X is generated by global sections); unless X is simple. “Simple“ means that there is no compact subvariety through the very general point of X and X not Kummer. Moreover we show that a compact Kähler threefold with only terminal singularities whose...

Varieties with generically nef tangent bundles

Thomas Peternell — 2012

Journal of the European Mathematical Society

We study various "generic" nefness and ampleness notions for holomorphic vector bundles on a projective manifold. We apply this in particular to the tangent bundle and investigate the relation to the geometry of the manifold.

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