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On compact Kähler surfaces

Nicholas Buchdahl (1999)

Annales de l'institut Fourier

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.

On the Kähler Rank of Compact Complex Surfaces

Matei Toma (2008)

Bulletin de la Société Mathématique de France

Harvey and Lawson introduced the Kähler rank and computed it in connection to the cone of positive exact currents of bidimension ( 1 , 1 ) for many classes of compact complex surfaces. In this paper we extend these computations to the only further known class of surfaces not considered by them, that of Kato surfaces. Our main tool is the reduction to the dynamics of associated holomorphic contractions ( 2 , 0 ) ( 2 , 0 ) .

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