Threefolds with quasi-projective universal cover

Benoît Claudon (1) , Andreas Höring (2)

1 IECN - Institut Élie Cartan de Nancy
2 IMJ - Institut de Mathématiques de Jussieu

We study compact Kähler threefolds X with infinite fundamental group whose universal cover can be compactified. Combining techniques from $L^2$ -theory, Campana's geometric orbifolds and the minimal model program we show that this condition imposes strong restrictions on the geometry of X. In particular we prove that if a projective threefold with infinite fundamental group has a quasi-projective universal cover, the latter is then isomorphic to the product of an affine space with a simply connected manifold.

Mots clés: Universal cover; L2 -theory; geometric orbifolds; MMP

Domaines: Géométrie algébrique [math.AG]

Benoît Claudon, Andreas Höring. Threefolds with quasi-projective universal cover. 2010. ⟨hal-00519394⟩