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Cônes positifs des variétés complexes compactes

Abstract : There are two notions of positivity for (1,1)-cohomology classes on a complex manifold: numerical effectivity, which is induced by the Lelong positivity at the level of differential forms, and pseudoeffectivity, which is a weaker property induced by the positivity of currents. In a first part, we build local obstructions to the numerical effectivity of a pseudoeffective cohomology class, which enables us to decompose it into a nef part and an exceptional divisor. We then consider the volume of a line bundle, which is an invariant measuring its positivity. We give a differential geometric interpretation of the volume, and we inscribe it into a ``mobile intersection'' theory, which only deals with the nef parts of the cohomology classes. Finally, we study the case when the manifold is a surface or is hyperkähler, where the geometry of the intersection form allows a more detailed description of these constructions.
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Contributor : Arlette Guttin-Lombard <>
Submitted on : Tuesday, January 14, 2003 - 2:56:13 PM
Last modification on : Wednesday, November 4, 2020 - 1:58:08 PM
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  • HAL Id : tel-00002268, version 1



Sébastien Boucksom. Cônes positifs des variétés complexes compactes. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2002. Français. ⟨tel-00002268⟩



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