A characterization of the Artin-Mumford curve

2015/01/12 by Arakelian, Nazar, Korchmáros, Gábor
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1501.02616

Abstract

Let M be the Artin-Mumford curve over the finite prime field \mathbbF_p with p>2. By a result of Valentini and Madan, Aut_\mathbbF_p(M)≅ H with H=(C_p× C_p)\rtimes D_p-1. We prove that if X is an algebraic curve of genus g=(p-1)² such that Aut_\mathbbF_p(X) contains a subgroup isomorphic to H then X is birationally equivalent over \mathbbF_p to the Artin-Mumford curve M.

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