Toward the structure of fibered fundamental groups of projective varieties
Toward the structure of fibered fundamental groups of projective varieties
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射影簇的纤维基本群的结构
DOI：
10.5802/jep.52
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
D. Arapura
中科院分区：
文献类型：
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作者：
D. Arapura
如果一个光滑射影簇的基本群映射到亏格为2或更多的光滑曲线的基本群上，则它的基本群是成纤维的。本文的目的是建立对这些群的一些强限制，特别是对Kodaira曲面的基本群。在Kodaira曲面的具体情况下，这些结果的形式是对映射类群的单行表示的限制。当单象由某些标准表示组成时，像是在一个厄米特型的半单群中是Zariski稠密的。
The fundamental group of a smooth projective variety is fibered if it maps onto the fundamental group of smooth curve of genus 2 or more. The goal of this paper is to establish some strong restrictions on these groups, and in particular on the fundamental groups of Kodaira surfaces. In the specific case of a Kodaira surface, these results are in the form of restrictions on the monodromy representation into the mapping class group. When the monodromy is composed with certain standard representations, the images are Zariski dense in a semisimple group of Hermitian type.