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Ahcène Lamari
Courants kählériens et surfaces compactes
Annales de l'institut Fourier, 49 no. 1 (1999), p. 263-285, doi: 10.5802/aif.1673
Article PDF | Reviews MR 2000d:32034 | Zbl 0926.32026 | 1 citation in Cedram

Résumé - Abstract

A compact complex surface is shown to be Kähler if and only if it carries a strictly positive $d$-closed current (in other words, a Kähler current), thanks to Demailly’s regularization theorem. We prove a Harvey-Lawson type characterization of compact manifolds carrying such a current. Using Hodge symmetry, we then give a unified proof of kählerianity for surfaces with even first Betti number.

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