Courants kählériens et surfaces compactes
Annales de l'Institut Fourier, Volume 49 (1999) no. 1, p. 263-285

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.

Le théorème de régularisation de Demailly ramène l’existence d’une métrique kählérienne sur une surface compacte à celle d’un (1-1)-courant strictement positif d-fermé (“courant kählérien”). Après avoir démontré un critère d’existence d’un tel courant, nous utilisons la symétrie de Hodge pour donner une démonstration unifiée du caractère kählérien des surfaces compactes à premier nombre de Betti pair.

@article{AIF_1999__49_1_263_0,
     author = {Lamari, Ahc\`ene},
     title = {Courants k\"ahl\'eriens et surfaces compactes},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {49},
     number = {1},
     year = {1999},
     pages = {263-285},
     doi = {10.5802/aif.1673},
     zbl = {0926.32026},
     mrnumber = {2000d:32034},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1999__49_1_263_0}
}
Courants kählériens et surfaces compactes. Annales de l'Institut Fourier, Volume 49 (1999) no. 1, pp. 263-285. doi : 10.5802/aif.1673. http://www.numdam.org/item/AIF_1999__49_1_263_0/

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