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Peter Roquette, Joachim Cuntz, David Masser, Tobias Colding, Daniel Huybrechts, Jun-Muk Hwang, Jakob Stix, Rainer Weissauer, Geordie Williamson, Franz Stückle

Abstract

In their paper from 2012, Bobadilla and Kollár studied topological conditions which guarantee that a proper map of complex algebraic varieties is a topological or differentiable fibration. They also asked whether a certain finiteness property on the relative covering space can imply that a proper map is a fibration. In this paper, we answer positively the integral homology version of their question in the case of abelian varieties, and the rational homology version in the case of compact ball quotients. We also propose several conjectures in relation to the Singer–Hopf conjecture in the complex projective setting.

Locations

• Journal für die reine und angewandte Mathematik (Crelles Journal) - View - PDF