Aspherical manifolds, Mellin transformation and a question of Bobadilla

Aspherical manifolds, Mellin transformation and a question of Bobadilla–Kollár

Published:2021-10-16 Issue:781 Volume:2021 Page:1-18
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Liu Yongqiang¹^ORCID,Maxim Laurenţiu²^ORCID,Wang Botong²

Affiliation:

1. The Institute of Geometry and Physics , University of Science and Technology of China , 96 Jinzhai Road , Hefei 230026 , P. R. China

2. Department of Mathematics , University of Wisconsin-Madison , 480 Lincoln Drive , Madison WI 53706-1388 , USA

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2021-0055/pdf

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