ball quotients
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Author(s):  
Yongqiang Liu ◽  
Laurenţiu Maxim ◽  
Botong Wang

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.


2019 ◽  
Vol 2019 (754) ◽  
pp. 253-279 ◽  
Author(s):  
Martin Deraux

Abstract We give an algebro-geometric construction of some of the non-arithmetic ball quotients constructed by the author, Parker and Paupert. The new construction reveals a relationship between the corresponding orbifold fundamental groups and the automorphism group of the Klein quartic, and also with groups constructed by Barthel–Hirzebruch–Höfer and Couwenberg–Heckman–Looijenga.


2019 ◽  
Vol 223 (3) ◽  
pp. 1123-1138 ◽  
Author(s):  
Samuel Boissière ◽  
Chiara Camere ◽  
Alessandra Sarti
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2018 ◽  
Vol 30 (2) ◽  
pp. 419-432
Author(s):  
Sai-Kee Yeung

AbstractThe purpose of this note is to show that{2K}of any smooth compact complex 2-ball quotient is very ample, except possibly for four pairs of fake projective planes of minimal type, whereKis the canonical line bundle. For the four pairs of fake projective planes, the sections of{2K_{M}}give an embedding ofMexcept possibly for at most two points onM.


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