Toward the structure of fibered fundamental groups of projective varieties

TL;DR

This paper investigates the structure of fibered fundamental groups of smooth projective varieties, establishing restrictions especially for Kodaira surfaces and analyzing monodromy representations into mapping class groups.

Contribution

It provides new restrictions on fibered fundamental groups and monodromy representations, enhancing understanding of their algebraic and geometric properties.

Findings

Restrictions on fundamental groups of Kodaira surfaces

Zariski density of monodromy images in semisimple groups

Insights into the structure of fibered fundamental groups

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.