Abelianity Conjecture for special threefolds

Abstract

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.

19 pages, 3 figures (in Appendix). Comments are wellcome

References in corpus (1)

• Orbifoldes speciales et classification bimeromorphe des varietes kaehleriennes compactes

Cited by in corpus (2)

• On the hyperbolicity of surfaces of general type with small $c_1^2$
• Asymptotically conical Calabi-Yau metrics on quasi-projective varieties