Moscow Mathematical Journal

Volume 16, Issue 4, October–December 2016 pp. 651–658.

Fundamental Group and Pluridifferentials on Compact Kähler Manifolds

Authors: Yohan Brunebarbe (1) and Frédéric Campana (2)
Author institution:(1) Ecole Polytechnique Fédérale de Lausanne, Lausanne, Chaire de Géométrie, Bâtiment MA, Station 8, CH 1015 Lausanne, Suisse
(2) Institut Elie Cartan, Université de Lorraine, 64, Boulevard des Aiguilletes, 54506-Vandoeuvre-les-Nancy, France, and Institut Universitaire de France KIAS (Seoul, South Korea)

Summary:

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: X → S between connected manifolds induces an isomorphism of fundamental groups if its smooth fibres are as above, and if X is Kähler.

2010 Math. Subj. Class. 14C30, 14J40, 14H30, 14F35, 32J18, 32J25, 32J27, 32Q30.

Keywords: Fundamental group, rationally connected manifolds, symmetric differentials, L² cohomology.

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