Algebraic varieties with quasi-projective universal cover

Benoît Claudon (1) , Andreas Höring (2) , János Kollár (3)

1 IECL - Institut Élie Cartan de Lorraine
2 IMJ - Institut de Mathématiques de Jussieu
3 Princeton University

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

Mots clés: universal cover; MMP

Domaines: Géométrie algébrique [math.AG]

Benoît Claudon, Andreas Höring, János Kollár. Algebraic varieties with quasi-projective universal cover. Journal für die reine und angewandte Mathematik, 2013, 679, pp.207-221. ⟨hal-00565667⟩