A. V. Ancona and V. Van-tan, On the blowing down problem in C-analytic geometry, J

B. Bauer, F. Campana, T. Eckl, and S. Kebekus, Thomas Peternell, S lawomir Rams, Tomasz Szemberg, and Lorenz Wotzlaw. A reduction map for nef line bundles, Complex geometry, pp.27-36, 2002.

C. Birkar, P. Cascini, C. D. Hacon, and J. Mckernan, Existence of minimal models for varieties of log general type, Journal of the American Mathematical Society, vol.23, issue.2, pp.405-468, 2010.
DOI : 10.1090/S0894-0347-09-00649-3

B. S. Boucksom, J. Demailly, P. Mihai, and T. Peternell, The pseudo-effective cone of a compact K??hler manifold and varieties of negative Kodaira dimension, Journal of Algebraic Geometry, vol.22, issue.2, pp.201-248, 2013.
DOI : 10.1090/S1056-3911-2012-00574-8

S. Boucksom, Divisorial Zariski decompositions on compact complex manifolds, Annales Scientifiques de l?????cole Normale Sup??rieure, vol.37, issue.1, pp.45-76, 2004.
DOI : 10.1016/j.ansens.2003.04.002

M. Brunella, A POSITIVITY PROPERTY FOR FOLIATIONS ON COMPACT K??HLER MANIFOLDS, International Journal of Mathematics, vol.17, issue.01, pp.35-43, 2006.
DOI : 10.1142/S0129167X06003333

F. Campana, OrbifoldesàOrbifoldesàpremì ere classe de Chern nulle, The Fano Conference, pp.339-351, 2004.

J. Cao, Abstract, Compositio Mathematica, vol.63, issue.11, pp.1869-1902, 2014.
DOI : 10.1353/ajm.2006.0044
URL : https://hal.archives-ouvertes.fr/hal-01199372

J. Cao and A. Höring, Rational curves on compact Kähler manifolds. arXiv preprint, 1502.03936, 2015. CHP16. Frédéric Campana, Andreas Höring, and Thomas Peternell. Abundance for Kähler threefolds, Annales de l'ENS, vol.49, pp.969-1023, 2016.

C. Tristan, V. Collins, and . Tosatti, Kähler currents and null loci, Invent. Math, vol.202, issue.3, pp.1167-1198

C. Tristan, V. Collins, and . Tosatti, A singular Demailly?P? aun theorem, C. R. Math. Acad. Sci. Paris, vol.354, issue.1, pp.91-95, 2016.

D. Demailly, Mesures de Monge-Amp??re et caract??risation g??om??trique des vari??t??s alg??briques affines, Mémoires de la Société mathématique de France, vol.1, pp.124-92, 1985.
DOI : 10.24033/msmf.320

J. Demailly, Regularization of closed positive currents and intersection theory, J. Algebraic Geom, vol.1, issue.3, pp.361-409, 1992.
DOI : 10.1007/978-3-663-14196-9_4
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.296.2912

J. Demailly, Multiplier ideal sheaves and analytic methods in algebraic geometry A Kawamata-Viehweg vanishing theorem on compact Kähler manifolds, School on Vanishing Theorems and Effective Results in Algebraic Geometry (Trieste, pp.1-148231, 2000.

J. Demailly, P. Mihai, and . Aun, Numerical characterization of the K??hler cone of a compact K??hler manifold, Annals of Mathematics, vol.159, issue.3, pp.1247-1274, 2004.
DOI : 10.4007/annals.2004.159.1247

S. Druel, A decomposition theorem for singular spaces with trivial canonical class of dimension at most five

I. Enoki, Stability and negativity for tangent sheaves of minimal K??hler spaces, Katata/Kyoto Lecture Notes in Math, vol.31, pp.118-126, 1987.
DOI : 10.1002/cpa.3160310304

A. Fujiki, On the structure of compact complex manifolds in C Osamu Fujino. Termination of 4-fold canonical flips, Algebraic varieties and analytic varieties, pp.231-302231, 1981.

F. O. Fujino, Addendum to: "Termination of 4-fold canonical flips", Classification of algebraic varieties, pp.251-257, 2005.
DOI : 10.2977/prims/1145475410

D. Greb, S. Kebekus, and T. Peternell, Singular spaces with trivial canonical class. arXiv preprint, to appear in Minimal models and extremal rays, Proceedings of the conference in honor of Shigefumi Mori's 60th birthday, Advanced Studies in Pure Mathematics, p.5250, 1110.

G. and H. Grauert, ???ber Modifikationen und exzeptionelle analytische Mengen, Mathematische Annalen, vol.126, issue.4, pp.331-368, 1962.
DOI : 10.1007/BF01441136

P. Graf, Algebraic approximation of Kähler threefolds of Kodaira dimension zero

X. Qi-'an-guan and . Zhou, A proof of Demailly's strong openness conjecture, Ann. of Math, vol.182, issue.22, pp.605-616, 2015.

A. Höring and T. Peternell, Mori fibre spaces for Kähler threefolds, J. Math. Sci. Univ. Tokyo, vol.22, issue.1, pp.219-246

A. Höring and T. Peternell, Minimal models for K??hler threefolds, Kaw82. Yujiro Kawamata, pp.217-26457, 1982.
DOI : 10.1007/s00222-015-0592-x

K. Y. Kawamata, Pluricanonical systems on minimal algebraic varieties, Inventiones Mathematicae, vol.119, issue.3, pp.567-588, 1985.
DOI : 10.1007/BF01388524

K. and Y. Kawamata, Minimal models and the Kodaira dimension of algebraic fiber spaces, J. Reine Angew. Math, vol.363, pp.1-46, 1985.

K. and Y. Kawamata, Abundance theorem for minimal threefolds, Inventiones Mathematicae, vol.26, issue.1, pp.229-246, 1992.
DOI : 10.1007/BF02100604

J. Kollár and S. Mori, Birational geometry of algebraic varieties, volume 134 of Cambridge Tracts in Mathematics, 1998.

K. , Y. Kawamata, K. Matsuda, and K. Matsuki, Introduction to the minimal model problem, Algebraic geometry, pp.283-360, 1985.

J. Kollár, Rational curves on algebraic varieties, volume 32 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, p.92, 1996.

J. Kollár, Flips and abundance for algebraic threefolds Papers from the Second Summer Seminar on Algebraic Geometry held at the University of Utah, Société Mathématique de France, 1991.

V. Lazi´clazi´c and T. Peternell, Abundance for varieties with many differential forms. arXiv preprint, 1601.

Y. Miyaoka, The Chern classes and Kodaira dimension of a minimal variety, Algebraic geometry, pp.449-476, 1985.

Y. Miyaoka and S. Mori, A Numerical Criterion for Uniruledness, The Annals of Mathematics, vol.124, issue.1, pp.65-69, 1986.
DOI : 10.2307/1971387

S. Mori, Projective Manifolds with Ample Tangent Bundles, The Annals of Mathematics, vol.110, issue.3, pp.593-606, 1979.
DOI : 10.2307/1971241

S. Mori, Threefolds Whose Canonical Bundles Are Not Numerically Effective, The Annals of Mathematics, vol.116, issue.1, pp.133-176, 1982.
DOI : 10.2307/2007050
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC349565

S. Mori, Flip theorem and the existence of minimal models for 3-folds, J. Amer. Math. Soc, vol.1, issue.1, pp.117-253, 1988.

N. Nakayama, The lower semicontinuity of the plurigenera of complex varieties, Algebraic geometry, pp.551-590, 1985.

Y. Namikawa, PROJECTIVITY CRITERION OF MOISHEZON SPACES AND DENSITY OF PROJECTIVE SYMPLECTIC VARIETIES, International Journal of Mathematics, vol.13, issue.02, pp.125-135, 2002.
DOI : 10.1142/S0129167X02001277

P. Mihai, Relative adjoint transcendental classes and albanese maps of compact kaehler manifolds with nef ricci curvature. arXiv preprint, 1209.

T. Peternell, Towards a Mori theory on compact K??hler threefolds III, Bulletin de la Société mathématique de France, vol.129, issue.3, pp.339-35695, 1992.
DOI : 10.24033/bsmf.2400
URL : http://arxiv.org/pdf/math/9902149v1.pdf

C. Voisin, On the homotopy types of compact K??hler and complex projective manifolds, Inventiones mathematicae, vol.14, issue.2, pp.329-343, 2004.
DOI : 10.1007/s00222-003-0352-1

C. Voisin, On integral Hodge classes on uniruled or Calabi-Yau threefolds Moduli spaces and arithmetic geometry, Advanced Studies in Pure Mathematics, vol.45, pp.43-73, 2006.

A. Höring, U. Côte-d-'azur, L. Cnrs, and E. France, -mail address: hoering@unice.fr Thomas Peternell, Mathematisches Institut