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.
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.
@article{AIF_1999__49_1_287_0, author = {Buchdahl, Nicholas}, title = {On compact {K\"ahler} surfaces}, journal = {Annales de l'Institut Fourier}, pages = {287--302}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {49}, number = {1}, year = {1999}, doi = {10.5802/aif.1674}, mrnumber = {2000f:32029}, zbl = {0926.32025}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1674/} }
TY - JOUR AU - Buchdahl, Nicholas TI - On compact Kähler surfaces JO - Annales de l'Institut Fourier PY - 1999 SP - 287 EP - 302 VL - 49 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1674/ DO - 10.5802/aif.1674 LA - en ID - AIF_1999__49_1_287_0 ER -
Buchdahl, Nicholas. On compact Kähler surfaces. Annales de l'Institut Fourier, Tome 49 (1999) no. 1, pp. 287-302. doi : 10.5802/aif.1674. http://archive.numdam.org/articles/10.5802/aif.1674/
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