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Comptes Rendus Mathématique
Volume 338, n° 1
pages 59-64 (janvier 2004)
Doi : 10.1016/j.crma.2003.11.011
Received : 12 November 2003 ; 
Estimation effective de la perte de positivité dans la régularisation des courants
Effective estimate of positivity loss in current regularizations

Dan  Popovici
Institut Fourier, bâtiment Maths Pures, 100, rue des Maths, BP 53, 38041 Grenoble cedex, France 


Soit   une variété hermitienne compacte et   un courant quasi-positif  -fermé de bidegré   sur   Une variante du théorème de régularisation de Demailly affirme que   est la limite faible d'une suite de courants   à singularités analytiques de coefficient  , dans la même classe de cohomologie que   avec des nombres de Lelong qui convergent vers ceux de   et avec une perte de positivité tendant vers zéro. Nous montrons que si la  -forme   est supposée fermée et de classe   les courants régularisants   peuvent être choisis de sorte que   pour une constante   indépendante de   Pour citer cet article : D. Popovici, C. R. Acad. Sci. Paris, Ser. I 338 (2004).


Let   be a compact complex Hermitian manifold, and let   be a  -closed   almost positive current on   A variant of Demailly's regularization-of-currents theorem states that   is the weak limit of a sequence of  -currents   with analytic singularities of coefficient  , lying in the same cohomology class as  , whose Lelong numbers converge to those of  , and with a loss of positivity decaying to zero. We prove that if the  -form   is assumed to be closed and   the regularizing currents   can be chosen such that   for a constant   independent of   To cite this article: D. Popovici, C. R. Acad. Sci. Paris, Ser. I 338 (2004).

© 2003  Académie des sciences@@#104156@@

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