Monodromy of Cyclic Coverings of the Projective Line

TL;DR

This paper investigates the monodromy action on the homology of cyclic coverings of the projective line, demonstrating that under certain conditions, the image forms an arithmetic group.

Contribution

It establishes that the monodromy group of cyclic coverings becomes arithmetic when the number of branch points exceeds a certain threshold.

Findings

Monodromy group is arithmetic for sufficiently many branch points.

The result applies to cyclic coverings of the projective line.

Provides conditions for the monodromy to be an arithmetic group.

Abstract

We show that the image of the pure braid group under the monodromy action on the homology of a cyclic covering of degree d of the projective line is an arithmetic group provided the number of branch points is sufficiently large compared to the degree.