Abelianity conjecture for special compact Kähler threefolds

Frédéric Campana (1) , Benoît Claudon (1)

1 IECL - Institut Élie Cartan de Lorraine

Using orbifold metrics of the appropriately signed Ricci curvature on orbifolds with negative or numerically trivial canonical bundle and the two-dimensional Log Minimal Model Program, we prove that the fundamental group of special compact Kähler threefolds is almost abelian. This property was conjectured in all dimensions in [Cam04b], and also for orbifolds in [Cam07], where the notion of specialness was introduced. We briefly recall below the definition, basic properties, and the role of special manifolds in classification theory.

Mots clés: Fundamental group of compact Kähler manifolds; Classification Theory; orbifold metrics; Log MMP

Domaines: Géométrie algébrique [math.AG]

Frédéric Campana, Benoît Claudon. Abelianity conjecture for special compact Kähler threefolds. Proceedings of the Edinburgh Mathematical Society, 2014, 57 (1), pp.55-78. ⟨10.1017/S0013091513000849⟩. ⟨hal-00605338⟩