On generalizations of Fermat curves over finite fields and their automorphisms

2016/08/15 by Arakelian, Nazar, Speziali, Pietro
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.04338

Abstract

Let X be an irreducible algebraic curve defined over a finite field \mathbbF_q of characteristic p>2. Assume that the \mathbbF_q-automorphism group of X admits as an automorphism group the direct product of two cyclic groups C_m and C_n of orders m and n prime to p such that both quotient curves X/C_n and X/C_m are rational. In this paper, we provide a complete classification of such curves, as well as a characterization of their full automorphism groups.

Related

• Automorphism groups of curves over arbitrary fields
• Automorphisms of the Generalized Fermat curves
• Constraints on the automorphism group of a curve
• The p-rank of curves of Fermat type
• Algebraic curves with automorphism groups of large prime order