Geodesic
Compact complex manifolds with numerically effective cotangent bundles
Documenta mathematica, Tome 2 (1997), pp. 183-193.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We prove that a projective manifold of dimension $n=2$ or 3 and Kodaira dimension 1 has a numerically effective cotangent bundle if and only if the Iitaka fibration is almost smooth, i.e. the only singular fibres are multiples of smooth elliptic curves ($n=2$) resp. multiples of smooth Abelian or hyperelliptic surfaces ($n=3$). In the case of a threefold which is fibred over a rational curve the proof needs an extra assumption concerning the multiplicities of the singular fibres. Furthermore, we prove the following theorem: let $X$ be a complex manifold which is hyberbolic with respect to the Carathéodory-Reiffen-pseudometric, then any compact quotient of $X$ has a numerically effective cotangent bundle.
Classification : 32C10, 32H20 
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     author = {Kratz, Henrik},
     title = {Compact complex manifolds with numerically effective cotangent bundles},
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Kratz, Henrik. Compact complex manifolds with numerically effective cotangent bundles. Documenta mathematica, Tome 2 (1997), pp. 183-193. http://geodesic.mathdoc.fr/item/DOCMA_1997__2__a8/