On compact Kähler surfaces
Annales de l'Institut Fourier, Volume 49 (1999) no. 1, p. 287-302

Without relying on the classification of compact complex surfaces, it is proved that every such surface with even first Betti number admits a Kähler metric and that a real form of the classical Nakai-Moishezon criterion holds on the surface.

Sans utiliser la classification des surfaces compactes complexes, on démontre qu’une telle surface dont le premier nombre de Betti est pair possède une métrique kählérienne, et qu’une version réelle du critère classique de Nakai-Moishezon est valable sur la surface.

@article{AIF_1999__49_1_287_0,
     author = {Buchdahl, Nicholas},
     title = {On compact K\"ahler surfaces},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {49},
     number = {1},
     year = {1999},
     pages = {287-302},
     doi = {10.5802/aif.1674},
     zbl = {0926.32025},
     mrnumber = {2000f:32029},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1999__49_1_287_0}
}
Buchdahl, Nicholas. On compact Kähler surfaces. Annales de l'Institut Fourier, Volume 49 (1999) no. 1, pp. 287-302. doi : 10.5802/aif.1674. http://www.numdam.org/item/AIF_1999__49_1_287_0/

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