Bounds on degrees of covers with injective monodromy in iterated Kodaira Fibrations

TL;DR

This paper establishes bounds on the index of subgroups with injective monodromy in the fundamental groups of iterated Kodaira fibrations, advancing understanding of their algebraic and geometric structure.

Contribution

It provides explicit bounds on the index of finite covers with injective monodromy in iterated Kodaira fibrations, answering a question posed by Llosa Isenrich and Py.

Findings

Derived explicit bounds on subgroup indices

Extended the understanding of monodromy in iterated fibrations

Connected algebraic properties with geometric structures

Abstract

Let $\pi:X\to Y$ be an $n$-dimensional iterated Kodaira fibration with fiber of genus $g$ and injective monodromy. Llosa Isenrich and Py proved that we can pass to a finite index subgroup of $\pi_1(X)$ to get the base space of an n+1-dimensional iterated Kodaira fibration with injective monodromy and they asked about bounding the index of such a group. We provide a bound on this index.