On automorphisms of algebraic curves
A. Broughton, T. Shaska, A. Wootton

TL;DR
This paper explores methods to determine the automorphism groups of algebraic curves of genus at least 2 over algebraically closed fields, providing explicit equations for these families when feasible.
Contribution
It introduces techniques for classifying automorphism groups of algebraic curves and supplies explicit equations for the associated families when possible.
Findings
Methods for determining automorphism groups are developed.
Explicit equations for families of curves with given automorphism groups are provided.
The approach applies to curves over fields of any characteristic.
Abstract
An irreducible, algebraic curve of genus defined over an algebraically closed field of characteristic , has finite automorphism group . In this paper we describe methods of determining the list of groups for a fixed . Moreover, equations of the corresponding families of curves are given when possible.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation
