Benoît Claudon

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

We extend to compact Kahler manifolds some classical results 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 Kahler case some general results on holomorphic convexity of coverings such as the linear Shafarevich conjecture.

Algebraic varieties with quasi-projective universal cover

Abstract We prove that the universal cover of a normal projective variety X is quasi-projective iff a finite étale cover of X is a fiber bundle over an Abelian variety with simply connected fiber.