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

Authors
  • Liu, Yongqiang1
  • Maxim, Laurenţiu2
  • Wang, Botong2
  • 1 University of Science and Technology of China, 96 Jinzhai Road, 230026 , (China)
  • 2 University of Wisconsin-Madison, 480 Lincoln Drive, WI 53706-1388 , (United States)
Type
Published Article
Journal
Journal für die reine und angewandte Mathematik (Crelles Journal)
Publisher
De Gruyter
Publication Date
Oct 16, 2021
Volume
2021
Issue
781
Pages
1–18
Identifiers
DOI: 10.1515/crelle-2021-0055
Source
De Gruyter
License
Yellow

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.

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