Arithmeticity of the monodromy of some Kodaira fibrations

被引：0

作者：

Salter, Nick ^{[1
]}

Tshishiku, Bena ^{[2
]}

机构：

[1] Columbia Univ, Dept Math, 2990 Broadway, New York, NY 10027 USA

[2] Brown Univ, Dept Math, 151 Thayer St, Providence, RI 02908 USA

来源：

COMPOSITIO MATHEMATICA | 2020年 / 156卷 / 01期

关键词：

surface bundles; monodromy; mapping class groups; arithmetic groups; SURFACE BUNDLES; REPRESENTATIONS;

D O I：

10.1112/S0010437X19007668

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A question of Griffiths Schmid asks when the monodromy group of an algebraic family of complex varieties is arithmetic. We resolve this in the affirmative for a class of algebraic surfaces known as Atiyah Kodaira manifolds, which have base and fibers equal to complete algebraic curves. Our methods are topological in nature and involve an analysis of the 'geometric' monodromy, valued in the mapping class group of the fiber.

引用

页码：114 / 157

页数：44