Smooth families of tori and linear Kähler groups. (English. French summary) Zbl 1414.32021

In a previous joint paper with F. Campana and P. Eyssidieux [J. Éc. Polytech., Math. 1, 331–342 (2014; Zbl 1312.32012)], the author proves that a linear Kähler group has a finite index subgroup which is projective. In this paper the previous result is improved, namely the main result is the proof that a Kähler group which is linear is also a projective one in the following sense: the fundamental group of a compact Kähler manifold can be realised as the fundamental group of a smooth projective variety if it is a linear group. The main tool of the proof is the study of the total space of a smooth family of tori endowed with a group action.


32Q15 Kähler manifolds
14D07 Variation of Hodge structures (algebro-geometric aspects)


Zbl 1312.32012
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