# Maximal rationally connected fibrations and movable curves

Luis E. Solá Conde^{[1]}; Matei Toma^{[2]}

- [1] Universidad Rey Juan Carlos Departamento de Matemáticas C. Tulipán s.n. 28933 Móstoles, Madrid (Spain)
- [2] Institut de Mathématiques Elie Cartan Nancy-Université B.P. 239 54506 Vandoeuvre-lès-Nancy Cedex (France) and Institute of Mathematics of the Romanian Academy

Annales de l’institut Fourier (2009)

- Volume: 59, Issue: 6, page 2359-2369
- ISSN: 0373-0956

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topSolá Conde, Luis E., and Toma, Matei. "Maximal rationally connected fibrations and movable curves." Annales de l’institut Fourier 59.6 (2009): 2359-2369. <http://eudml.org/doc/10457>.

@article{SoláConde2009,

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.},

affiliation = {Universidad Rey Juan Carlos Departamento de Matemáticas C. Tulipán s.n. 28933 Móstoles, Madrid (Spain); Institut de Mathématiques Elie Cartan Nancy-Université B.P. 239 54506 Vandoeuvre-lès-Nancy Cedex (France) and Institute of Mathematics of the Romanian Academy},

author = {Solá Conde, Luis E., Toma, Matei},

journal = {Annales de l’institut Fourier},

keywords = {Uniruled variety; maximal rationally connected fibration; movable curve; Harder-Narasimhan filtration; uniruled variety; rationally connected fibration},

language = {eng},

number = {6},

pages = {2359-2369},

publisher = {Association des Annales de l’institut Fourier},

title = {Maximal rationally connected fibrations and movable curves},

url = {http://eudml.org/doc/10457},

volume = {59},

year = {2009},

}

TY - JOUR

AU - Solá Conde, Luis E.

AU - Toma, Matei

TI - Maximal rationally connected fibrations and movable curves

JO - Annales de l’institut Fourier

PY - 2009

PB - Association des Annales de l’institut Fourier

VL - 59

IS - 6

SP - 2359

EP - 2369

AB - 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.

LA - eng

KW - Uniruled variety; maximal rationally connected fibration; movable curve; Harder-Narasimhan filtration; uniruled variety; rationally connected fibration

UR - http://eudml.org/doc/10457

ER -

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