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arXiv · 1510.07922

Fundamental group and pluridifferentials on compact Kähler manifolds

Yohan Brunebarbe·Frédéric Campana
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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.

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Yohan Brunebarbe, Frédéric Campana. 2015-11-05. Fundamental group and pluridifferentials on compact Kähler manifolds. https://arxiv.org/abs/1510.07922

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