Abstract
Let X be a compact n-dimensional complex manifold and let T be a closed positive current of bidegree (1, 1) on X. In general, T cannot be approximated by closed positive currents of class C ∞: a necessary condition for this is that the cohomology class {T} is numerically effective in the sense that ∫ Y {T}P ≥ 0 for every p-dimensional subvariety Y ⊂ X. For example, if E ≃ ℙn−1 is the exceptional divisor of a one-point blow-up X → X′, then T = [E] cannot be positively approximated: for every curve C ⊂ E, we have ∫ C {E} = ∫ C c 1(O(−1)) < 0. However, we will see that it is always possible to approximate a closed positive current T of type (1, 1) by closed real currents admitting a small negative part, and that this negative part can be estimated in terms of the Lelong numbers of T and the geometry of X.
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Dedicated to Professor Pierre Dolbeault on the occasion of his retirement
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© 1994 Springer Fachmedien Wiesbaden
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Demailly, JP. (1994). Regularization of closed positive currents of type (1,1) by the flow of a Chern connection. In: Skoda, H., Trépreau, JM. (eds) Contributions to Complex Analysis and Analytic Geometry / Analyse Complexe et Géométrie Analytique. Aspects of Mathematics, vol E 26. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14196-9_4
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DOI: https://doi.org/10.1007/978-3-663-14196-9_4
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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