. [. Bibliographie, S. Araujo, S. J. Druel, and . Kovács, Cohomological characterizations of projective spaces and hyperquadrics, Invent. Math, vol.174, pp.233-253, 2008.

]. D. Akh95 and . Akhiezer, Lie Group Actions in Complex Analysis, Aspects of math, 1995.

J. [. Araujo and . Kollár, Rational Curves on Varieties, Higher Dimensional Varieties and Rational Points, 2001.
DOI : 10.1007/978-3-662-05123-8_3

]. C. Ar06 and . Araujo, Rational curves of minimal degree and characterizations of projective spaces, Math. Ann, vol.335, issue.4, pp.937-951, 2006.

J. [. Andreatta and . Wi´sniewskiwi´sniewski, On manifolds whose tangent bundle contains an ample subbundle, Inventiones mathematicae, vol.146, issue.1, pp.209-217, 2001.
DOI : 10.1007/PL00005808

C. [. Bonavero and S. Casagrande, On covering and quasi-unsplit families of curves, Journal of the European Mathematical Society, vol.9, issue.1, pp.45-57, 2007.
DOI : 10.4171/JEMS/71

URL : https://hal.archives-ouvertes.fr/hal-00380922

J. [. Boucksom, M. Demailly, and T. Pa?unpa?un, The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension, arXiv :math, p.405285, 2004.

]. A. Be00 and . Beauville, Symplectic singularities, Invent. Math, vol.139, pp.541-549, 2000.

H. [. Birkenhake and . Lange, Complex abelian varieties, 1992.
DOI : 10.1007/978-3-662-06307-1

M. [. Bogomolov and . Mcquillan, Rational Curves on Foliated Varieties, IHES Preprint, vol.183, 2001.
DOI : 10.2307/1971387

J. [. Burns-jr and . Wahl, Local contributions to global deformations of surfaces, Inventiones Mathematicae, vol.87, issue.1, pp.67-88, 1974.
DOI : 10.1007/BF01406846

]. F. Ca92 and . Campana, Connexité rationnelle des variétés de Fano, Ann. Sci. ENS, vol.25, pp.539-545, 1992.

H. [. Campana and . Flenner, A characterization of ample vector bundles on a curve, Mathematische Annalen, vol.77, issue.1, pp.571-575, 1990.
DOI : 10.1007/BF01446914

T. [. Campana, Projective manifolds whose tangent bundles are numerically effective, Mathematische Annalen, vol.19, issue.1, pp.169-187, 1991.
DOI : 10.1007/BF01446566

F. Campana and T. , Rational curves and ampleness properties??of the tangent bundle of algebraic varieties, manuscripta mathematica, vol.97, issue.1, pp.59-74, 1998.
DOI : 10.1007/s002290050085

]. O. De01 and . Debarre, Higher-Dimensional Algebraic Geometry, 2001.

T. [. Demailly, M. Peternell, and . Schneider, Compact complex manifolds with numerically effective tangent bundles, J. Alg. Geom, vol.3, issue.2, pp.295-345, 1994.

T. [. Demailly, M. Peternell, and . Schneider, Holomorphic line bundles with partially vanishing cohomology, Conf, Israel Mathematical conference Proceedings, vol.9, pp.165-198, 1996.

T. [. Demailly, M. Peternell, and . Schneider, PSEUDO-EFFECTIVE LINE BUNDLES ON COMPACT K??HLER MANIFOLDS, International Journal of Mathematics, vol.12, issue.06, pp.689-741, 2001.
DOI : 10.1142/S0129167X01000861

]. S. Dr04 and . Druel, Caractérisation de l'espace projectif, Manuscripta Math, vol.115, issue.1, pp.19-30, 2004.

R. [. Ein, M. Lazarsfeld, M. Musta¸t?amusta¸t?musta¸t?a, M. Nakamaye, and . Popa, Invariants asymptotiques des lieux de base, Annales de l???institut Fourier, vol.56, issue.6, p.308116, 2003.
DOI : 10.5802/aif.2225

]. H. Fl84 and . Flenner, Restrictions of semistable bundles on projective varieties, Commentarii Mathematici Helvetici, vol.59, 1984.

]. T. Fu75 and . Fujita, On the structure of polarized varieties with ?-genera zero, J. Fac. Sci. Univ. Tokyo, Sect. IA Math, vol.22, pp.103-115, 1975.

]. A. Gr65 and . Grothendieck, ´ Eléments de géométrie algébrique IV. ´ Etude locale des schémas et des morphismes de schémas, Seconde partie, Inst. HautesÉtudes Hautes´HautesÉtudes Sci. Publ. Math. tome, vol.24, pp.5-231, 1965.

]. R. Ha77 and . Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, vol.52, 1977.

]. R. Ha82 and . Hartshorne, Stable reflexive sheaves, Invent. Math, vol.66, pp.165-190, 1982.

M. [. Huybrechts and . Lehn, The geometry of moduli spaces of sheaves, Aspects of math, vol.31, 1997.

N. Hwang and . Mok, BIRATIONALITY OF THE TANGENT MAP FOR MINIMAL RATIONAL CURVES, Asian Journal of Mathematics, vol.8, issue.1, pp.51-63, 2004.
DOI : 10.4310/AJM.2004.v8.n1.a6

M. [. Harder and . Narasimhan, On the cohomology groups of moduli spaces of vector bundles on curves, Mathematische Annalen, vol.95, issue.3, pp.215-248, 1975.
DOI : 10.1007/BF01357141

]. S. Ke02 and . Kebekus, Families of singular rational curves, J. Algebr. Geom, vol.11, issue.2, pp.245-256, 2002.

J. Kollár, Y. Miyaoka, and S. Mori, Rationally Connected Varieties, J. Algebr. Geom, vol.1, issue.3, pp.429-448, 1992.
DOI : 10.1007/978-3-662-03276-3_5

J. Kollár, Y. Miyaoka, and S. Mori, Rational connectedness and boundedness of Fano manifolds, Journal of Differential Geometry, vol.36, issue.3, pp.765-779, 1992.
DOI : 10.4310/jdg/1214453188

S. Kobayashi, Differential Geometry of Complex Vector Bundles, Publications of the Math. Society of, Japan, vol.15, 1987.

]. J. Kol96 and . Kollár, Rational Curves on Algebraic Varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge, 1996.

L. [. Kebekus, M. Solá-conde, and . Toma, Rationally connected foliations after Bogomolov and McQuillan, Journal of Algebraic Geometry, vol.16, issue.1, pp.65-81, 2007.
DOI : 10.1090/S1056-3911-06-00435-8

URL : http://arxiv.org/abs/math/0505222

]. R. La04 and . Lazarsfeld, Positivity in algebraic geometry I-II, Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge, 2004.

]. S. Mo79 and . Mori, Projective manifolds with ample tangent bundle, Ann. of Math, vol.110, issue.3, pp.593-606, 1979.

A. [. Mehta and . Ramanathan, Semistable sheaves on projective varieties and their restriction to curves, Mathematische Annalen, vol.128, issue.3, pp.213-224, 1982.
DOI : 10.1007/BF01450677

M. [. Okonek, H. Schneider, and . Splinder, Vector bundles on projective spaces, 1980.
DOI : 10.1007/978-3-0348-0151-5

]. T. Pe08 and . Peternell, Varieties with generically nef tangent bundles, 2008.

. [. Shepherd-barron, Miyaoka's theorems on the generic seminegativity of T X , in Flips and abundance for algebraic threefolds, Astérisque, vol.211, pp.103-115, 1992.

]. J. Ser66 and . Serre, Prolongement de faisceaux analytiques cohérents, Annales de l'Institut Fourier, tome 16, pp.363-374, 1966.

]. J. Wa83 and . Wahl, A cohomological characterization of P n, Invent. Math, vol.72, issue.2, pp.315-322, 1983.