Estimation effective de la perte de positivité dans la régularisation des courants

Abstract

Let ( X, ω) be a compact complex Hermitian manifold, and let T⩾ γ be a d-closed (1,1) almost positive current on X. A variant of Demailly's regularization-of-currents theorem states that T is the weak limit of a sequence of (1,1)-currents T m with analytic singularities of coefficient 1/ m, lying in the same cohomology class as T, whose Lelong numbers converge to those of T, and with a loss of positivity decaying to zero. We prove that if the (1,1)-form γ is assumed to be closed and C ∞, the regularizing currents T m can be chosen such that T m⩾γ− C m for a constant C>0 independent of m. To cite this article: D. Popovici, C. R. Acad. Sci. Paris, Ser. I 338 (2004).