Compact complex manifolds with numerically effective cotangent bundles
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.
scientific article; zbMATH DE number 1139207