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Maximal rationally connected fibrations and movable curves

Luis E. Solá Conde, Matei Toma (2009)

Annales de l’institut Fourier

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...

Moduli of Germs of Legendrian Curves

António Araújo, Orlando Neto (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

We construct the generic component of the moduli space of the germs of Legendrian curves with generic plane projection topologically equivalent to a curve y n = x m .

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