Mod-$\ell$ monodromy of double covers of $\mathbb{P}^n$ branched along hyperplane arrangements

TL;DR

This paper investigates the mod-$\,\ell$ geometric monodromy groups associated with universal double covers of projective space branched along hyperplane arrangements, providing new insights into their structure.

Contribution

It determines the mod-$\ell$ monodromy groups for a broad class of double covers, advancing understanding of their algebraic and geometric properties.

Findings

Identifies the mod-$\ell$ monodromy group for general hyperplane arrangements.

Provides explicit descriptions of the monodromy in the universal family.

Enhances understanding of the algebraic structure of branched double covers.

Abstract

We determine the mod-$\ell$ geometric monodromy group of the universal family of double covers of projective space branched along hyperplane arrangements in general position.