A compact complex surface is shown to be Kähler if and only if it carries a strictly positive -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 -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}, pages = {263--285}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {49}, number = {1}, year = {1999}, doi = {10.5802/aif.1673}, mrnumber = {2000d:32034}, zbl = {0926.32026}, language = {fr}, url = {http://archive.numdam.org/articles/10.5802/aif.1673/} }
TY - JOUR AU - Lamari, Ahcène TI - Courants kählériens et surfaces compactes JO - Annales de l'Institut Fourier PY - 1999 SP - 263 EP - 285 VL - 49 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1673/ DO - 10.5802/aif.1673 LA - fr ID - AIF_1999__49_1_263_0 ER -
Lamari, Ahcène. Courants kählériens et surfaces compactes. Annales de l'Institut Fourier, Volume 49 (1999) no. 1, pp. 263-285. doi : 10.5802/aif.1673. http://archive.numdam.org/articles/10.5802/aif.1673/
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