Fundamental group and pluridifferentials on compact Kähler manifolds

2015/10/27 by Brunebarbe, Yohan, Campana, Frédéric
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.07922

Abstract

A compact Kähler manifold is shown to be simply-connected if its `symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective connected holomorphic map between connected complex manifolds induces an isomorphism of fundamental groups if its smooth fibres are as above, and if the domain is Kähler.

Related

• Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature
• The fundamental group, rational connectedness and the positivity of Kaehler manifolds
• Homomorphisms between fundamental groups of Kähler manifolds
• Fibred K"ahler and quasi-projective Groups
• Mapping Class Groups of Simply Connected Kähler Manifolds