Maximal rationally connected fibrations and movable curves

Details Maximal rationally connected fibrations and movable curves Maximal rationally connected fibrations and movable curves

2008-11-13

arxiv.org/abs/0811.2141v2

Mathematics

Algebraic Geometry

An error in the argumentation has been corrected

Scientific paper

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.

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