Étant donnée une variété kählérienne compacte , on étudie dans l’espace vectoriel réel de cohomologie de Dolbeault le cône convexe des classes de Kähler ainsi que celui, plus grand, des classes de courants positifs fermés de type . Lorsque est projective, les traces de ces cônes sur l’espace de Néron-Severi 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 be a compact Kähler manifold. In the real vector space of Dolbeault cohomology classes of type , we study the convex cone of Kähler classes and the larger cone of classes of positive closed currents of type . When is projective, theses cones cut out, on the Néron-Severi subspace generated by integral classes, the cone of classes of ample divisors and the closure of the cone of classes of effective divisors.
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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