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

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.

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

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