%0 Journal Article
%T Maximal rationally connected fibrations and movable curves
%A Luis Eduardo Sola Conde
%A Matei Toma
%J Mathematics
%D 2008
%I arXiv
%X A well known result of Miyaoka asserts that a complex projective manifold is uniruled if its cotangent bundle restricted to a general complete intersection curve is not nef. Using the Harder-Narasimhan filtration of the tangent bundle, it can moreover be shown that the choice of such a curve gives rise to a rationally connected foliation of the manifold. In this note we show that, conversely, a movable curve can be found so that the maximal rationally connected fibration of the manifold may be recovered as a term of the associated Harder-Narasimhan filtration of the tangent bundle.
%U http://arxiv.org/abs/0811.2141v2