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
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://archive.numdam.org/item/SB_2004-2005__47__199_0/

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