Classes de cohomologie positives dans les variétés kählériennes compactes  [ Positive cohomology classes in compact Kähler varieties ]
Séminaire Bourbaki : volume 2004/2005, exposés 938-951, Astérisque no. 307  (2006), Talk no. 943, p. 199-228

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.

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.

Classification:  32J27,  14M20,  14E30,  14C20,  14C17,  14C30,  32C30
Keywords: Kähler manifold, hyperkähler manifold, ample cone, nef cone, pseudo-effective cone, big cone, Kähler cone, current, singular metric, Zariski decomposition, volume of a line bundle, uniruled variety, mobile curve
@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},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {307},
     year = {2006},
     note = {talk:943},
     pages = {199-228},
     zbl = {1125.32009},
     mrnumber = {2296419},
     language = {fr},
     url = {http://www.numdam.org/item/SB_2004-2005__47__199_0}
}
Debarre, Olivier. Classes de cohomologie positives dans les variétés kählériennes compactes, in Séminaire Bourbaki : volume 2004/2005, exposés 938-951, Astérisque, no. 307 (2006), Talk no. 943, pp. 199-228. http://www.numdam.org/item/SB_2004-2005__47__199_0/

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