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Abelianity Conjecture for Special Compact Kähler 3-Folds

Published online by Cambridge University Press:  19 December 2013

Fréderic Campana  and
Benoît Claudon
Fréderic Campana
Affiliation:
Institut Élie Cartan Nancy, Université Henri Poincaré Nancy 1, BP 70239, 54506 Vandoeuvre-lès-Nancy Cedex, France, ([email protected]; [email protected])
Benoît Claudon
Affiliation:
Institut Élie Cartan Nancy, Université Henri Poincaré Nancy 1, BP 70239, 54506 Vandoeuvre-lès-Nancy Cedex, France, ([email protected]; [email protected])
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Abstract

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Using orbifold metrics of the appropriately signed Ricci curvature on orbifolds with a negative or numerically trivial canonical bundle and the two-dimensional log minimal model programme, we prove that the fundamental group of special compact Kähler 3-folds is almost abelian. This property was conjectured in all dimensions by Campana in 2004, and also for orbifolds in 2007, where the notion of specialness was introduced. We briefly recall the definition, basic properties and the role of special manifolds in classification theory.

Keywords

Special compact Kähler 3-foldsfundamental grouptwo-dimensional special orbifoldsklt singularitiesPrimary 32J2714J30Secondary 14F3514J1732J1732Q55
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 1 , February 2014 , pp. 55 - 78
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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