On the Group of Automorphisms of Cyclic Covers of the Riemann Sphere

2003/10/04 by Sadok Kallel, Kallel, Sadok, Denis Sjerve +1
Mathematics · #14H37 #14H45 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR #msc:14H37 #msc:14H45

paper · pdf · doi:10.48550/arxiv.math/0310053

23 pages, 1 figure

arxiv created 2003/10/04 · arxiv updated 2009/12/01

Abstract

This note uses some recent calculations of Conder and Bujalance (on classifying finite index group extensions of Fuchsian groups with abelian quotient and torsion free kernel) in order to determine the full automorphism groups of some cylic coverings of the line (including curves of Fermat and Lefschetz type). The answer is complete for cyclic covers that branch over three points.

Related

• On cyclic covers of the projective line
• Bounds for the order of automorphism groups of cyclic covering fibrations of an elliptic surface
• Automorphisms groups for p-cyclic covers of the affine line
• Bounds for the order of automorphism groups of cyclic covering fibrations of a ruled surface
• The automorphism group of Kodaira surfaces