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arXiv · 2203.13499

On Lelong Numbers of Generalized Monge-Ampère Products

Martin Sera
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Abstract

We consider generalized (mixed) Monge-Ampère products of quasiplurisubharmonic functions (with and without analytic singularities) as they were introduced and studied in several articles written by subsets of M. Andersson, E. Wulcan, Z. Błocki, R. Lärkäng, H. Raufi, J. Ruppenthal, and the author. We continue these studies and present estimates for the Lelong numbers of pushforwards of such products by proper holomorphic submersions. Furthermore, we apply these estimates to Chern and Segre currents of pseudoeffective vector bundles. Among other corollaries, we obtain the following generalization of a recent result by X. Wu. If the non-nef locus of a pseudoeffective vector bundle $E$ on a Kähler manifold is contained in a countable union of $k$-codimensional analytic sets, and if the $k$-power of the first Chern class of $E$ is trivial, then $E$ is nef.

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Martin Sera. 2023-06-28. On Lelong Numbers of Generalized Monge-Ampère Products. https://doi.org/10.1007/s00209-023-03284-9

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