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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.

Orbifolds, special varieties and classification theory

Frédéric Campana (2004)

Annales de l’institut Fourier

This article gives a description, by means of functorial intrinsic fibrations, of the geometric structure (and conjecturally also of the Kobayashi pseudometric, as well as of the arithmetic in the projective case) of compact Kähler manifolds. We first define special manifolds as being the compact Kähler manifolds with no meromorphic map onto an orbifold of general type, the orbifold structure on the base being given by the divisor of multiple fibres. We next show that rationally connected Kähler...

Orbifolds, special varieties and classification theory: an appendix

Frédéric Campana (2004)

Annales de l’institut Fourier

For any compact Kähler manifold X and for any equivalence relation generated by a symmetric binary relation with compact analytic graph in X × X , the existence of a meromorphic quotient is known from Inv. Math. 63 (1981). We give here a simplified and detailed proof of the existence of such quotients, following the approach of that paper. These quotients are used in one of the two constructions of the core of X given in the previous paper of this fascicule, as well as in many other questions.

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