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arXiv · 0811.2141

Maximal rationally connected fibrations and movable curves

Luis Eduardo Sola Conde·Matei Toma
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Abstract

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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Luis Eduardo Sola Conde, Matei Toma. 2008-11-13. Maximal rationally connected fibrations and movable curves. https://arxiv.org/abs/0811.2141

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