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 H1,1(X,𝐑)H2(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)𝐑H1,1(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 H1,1(X,𝐑)H2(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)𝐑H1,1(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
Mot 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
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
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     title = {Classes de cohomologie positives dans les vari\'et\'es k\"ahl\'eriennes compactes},
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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://www.numdam.org/item/SB_2004-2005__47__199_0/

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