Toward the structure of fibered fundamental groups of projective varieties

2015/10/26 by Arapura, Donu
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.07692

Abstract

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.

Related

• Fibred K"ahler and quasi-projective Groups
• Kodaira fibrations and beyond: methods for moduli theory
• Real Kodaira surfaces
• Fundamental groups of strata of abelian differentials of low codimension
• Kodaira fibrations, Kähler groups, and finiteness properties