Représentations linéaires des groupes kählériens : factorisations et conjecture de Shafarevich linéaire

Fréderic Campana (1) , Benoît Claudon (1) , Philippe Eyssidieux (2)

1 IECL - Institut Élie Cartan de Lorraine
2 IF - Institut Fourier

We extend to compact Kähler manifolds some classical re-sults on linear representation of fundamental groups of complex projective manifolds. Our approach based on an interversion lemma for fibrations with tori versus general type manifolds as fibers gives a refinement of the classical work of Zuo. We extend to the Kähler case some general results on holomorphic convexity of coverings such as the linear Shafarevich conjecture.

Mots clés: Kähler manifolds; Kähler groups; holomorphic convexity; Shafarevich morphisms

Domaines: Géométrie algébrique [math.AG]

Fréderic Campana, Benoît Claudon, Philippe Eyssidieux. Représentations linéaires des groupes kählériens : factorisations et conjecture de Shafarevich linéaire. Compositio Mathematica, 2014, 151 (2), pp.351-376. ⟨10.1112/S0010437X14007751⟩. ⟨hal-01094110⟩