Classes de cohomologie positives dans les variétés kählériennes compactes
Séminaire Bourbaki : volume 2004/2005, exposés 938-951, Astérisque, no. 307 (2006), Exposé no. 943, pp. 199-228.

Étant donnée une variété kählérienne compacte X, on étudie dans l’espace vectoriel réel de cohomologie de Dolbeault H 1,1 (X,𝐑)⊂H 2 (X,𝐑) le cône convexe des classes de Kähler ainsi que celui, plus grand, des classes de courants positifs fermés de type (1,1). Lorsque X est projective, les traces de ces cônes sur l’espace de Néron-Severi NS (X) 𝐑 ⊂H 1,1 (X,𝐑) engendré par les classes entières sont respectivement le cône des classes de diviseurs amples et l’adhérence de celui des classes de diviseurs effectifs.

Let X be a compact Kähler manifold. In the real vector space H 1,1 (X,𝐑)⊂H 2 (X,𝐑) of Dolbeault cohomology classes of type (1,1), we study the convex cone of Kähler classes and the larger cone of classes of positive closed currents of type (1,1). When X is projective, theses cones cut out, on the Néron-Severi subspace NS (X) 𝐑 ⊂H 1,1 (X,𝐑) generated by integral classes, the cone of classes of ample divisors and the closure of the cone of classes of effective divisors.

Classification : 32J27,  14M20,  14E30,  14C20,  14C17,  14C30,  32C30
Mots clés : variété kählérienne, variété hyperkählérienne, cône ample, cône nef, cône pseudo-effectif, classes grandes, cône de Kähler, courant, métrique singulière, décomposition de Zariski, volume d'un fibré en droites, variété uniréglée, courbe mobile 
@incollection{SB_2004-2005__47__199_0,
     author = {Debarre, Olivier},
     title = {Classes de cohomologie positives dans les vari\'et\'es k\"ahl\'eriennes compactes},
     booktitle = {S\'eminaire Bourbaki : volume 2004/2005, expos\'es 938-951},
     author = {Collectif},
     series = {Ast\'erisque},
     note = {talk:943},
     pages = {199--228},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {307},
     year = {2006},
     zbl = {1125.32009},
     mrnumber = {2296419},
     language = {fr},
     url = {archive.numdam.org/item/SB_2004-2005__47__199_0/}
}
Debarre, Olivier. Classes de cohomologie positives dans les variétés kählériennes compactes, dans Séminaire Bourbaki : volume 2004/2005, exposés 938-951, Astérisque, no. 307 (2006), Exposé no. 943, pp. 199-228. http://archive.numdam.org/item/SB_2004-2005__47__199_0/

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