Presentation

Full Automorphism Groups of Cyclic n-gonal Surfaces

UNED Geometry Seminar
(2009)
Abstract

Cyclic

*n*-gonal Riemann surfaces,*S,*are of great interest since they are algebraic curves defined by*y^n = f(x)*for some polynomial*f(x)*. For*n=2*the surfaces are hyperelliptic surfaces, which are very well studied. The cases for small*n*or*n*a prime are also well studied. The cyclic*n*-gonal surface*S*has a cyclic group*C*of automorphisms generalizing the notion of hyperelliptic involution. Under reasonable hypotheses the group*C*is a normal subgroup of the full group of automorphisms of*S*when the genus is large. If*C*is normal then the determination of the full automorphism then reverts to a careful analysis of the finite groups of automorphisms of the sphere. In this talk we are going to extend the problem of determining the full automorphism group

*A*of a cyclic*n*-gonal surface*S*under assumption of weak normality, i.e., that for any non-trivial*H < C*, the normalizers of*H*and*C*in*A*are equal. This assumption automatically holds when*n*is a prime. Again in this case the group is normal when the genus is large enough with respect to*n*. We will focus on the exceptional, low genus cases.Keywords

- Riemann surface,
- cyclic n-gonal surface,
- automorphism of surface

Disciplines

Publication Date

February 26, 2009
Location

UNED, Madrid, Spain
Citation Information

Sean A Broughton and Aaron Wootton. "Full Automorphism Groups of Cyclic n-gonal Surfaces" *UNED Geometry Seminar*(2009)

Available at: http://works.bepress.com/allen_broughton/70/

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