A finiteness property on monodromies of holomorphic families

TL;DR

This paper investigates the set of monodromy representations of holomorphic families of curves associated with Kahler groups, focusing on their finiteness properties and structural characteristics.

Contribution

It introduces a finiteness property for monodromies of holomorphic curve families related to Kahler groups, providing new insights into their algebraic and geometric structure.

Findings

Identifies conditions under which monodromies are finite

Establishes structural constraints on monodromy representations

Connects monodromy properties with Kahler group characteristics

Abstract

Given a Kahler group, we study the set of homomorphisms from this group to the mapping class group which can be realized as the monodromy of a holomorphic family of curves.