Abstract
Let X be a compact Kähler manifold of dimension k and T be a positive closed current on X of bidimension (p,p) (1≤p<k−1). We construct a continuous linear transform ℒ p (T) of T which is a positive closed current on X of bidegree (1,1) which has the same Lelong numbers as T. We deduce from that construction self-intersection inequalities for positive closed currents of any bidegree.
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Vigny, G. Lelong-Skoda Transform for Compact Kähler Manifolds and Self-Intersection Inequalities. J Geom Anal 19, 433–451 (2009). https://doi.org/10.1007/s12220-008-9056-5
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DOI: https://doi.org/10.1007/s12220-008-9056-5