论文标题
非球形流形，梅林转化和巴巴迪拉·科拉尔的问题
Aspherical manifolds, Mellin transformation and a question of Bobadilla-Kollár
论文作者
论文摘要
在他们的2012年论文中，Bobadilla和Kollár研究了拓扑条件，这些条件确保了合适的复杂代数品种图是拓扑或可区分的纤维化。他们还询问相对覆盖空间上的某些有限属性是否可能暗示正确的地图是纤维化。在本文中，我们在Abelian品种的情况下积极回答其问题的整体同源版本，以及在紧凑型球员的情况下的理性同源性版本。我们还提出了与复杂的投影设置中有关歌手-HOPF猜想的几种猜想。
In their 2012 paper, 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.
