Monodromy of Cyclic Coverings of the Projective Line

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.

47 pages (to appear in Inventiones Mathematicae)

Cited by in corpus (6)

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• Zariski density of monodromy groups via Picard-Lefschetz type formula
• The Burau representation and shapes of polyhedra
• Sums of Fractions and Finiteness of Monodromy
• Finiteness of hyperelliptic and superelliptic curves with CM Jacobians
• Big monodromy for higher Prym representations