This article is cited in 6 papers

Fundamental group and pluridifferentials on compact Kähler manifolds

Yohan Brunebarbe^a, Frédéric Campana<sup>bcd

a</sup> Ecole Polytechnique Fédérale de Lausanne, Lausanne, Chaire de Géométrie, Bâtiment MA, Station 8, CH 1015 Lausanne, Suisse
^b Institut Elie Cartan, Université de Lorraine, 64, Boulevard des Aiguilletes, 54506-Vandoeuvre-les-Nancy, France
^c Institut Universitaire de France
^d KIAS (Seoul, South Korea)

Abstract: A compact Kähler manifold $X$ 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 $f\colon X\to S$ between connected manifolds induces an isomorphism of fundamental groups if its smooth fibres are as above, and if $X$ is Kähler.

Key words and phrases: fundamental group, rationally connected manifolds, symmetric differentials, $L^2$ cohomology.

MSC: 14C30, 14J40, 14H30, 14F35, 32J18, 32J25, 32J27, 32Q30

Received: October 26, 2015; in revised form June 5, 2016

Language: English

DOI: 10.17323/1609-4514-2016-16-4-651-658

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