Let M be the Artin–Mumford curve over the finite prime field Fp with p>2. By a result of Valentini and Madan, AutFp(M)≅H with H=(Cp×Cp)⋊Dp−1. We prove that if X is an algebraic curve of genus g=(p−1)2 defined over Fp such that AutFp(X) contains a subgroup isomorphic to H then X is birationally equivalent over Fp to the Artin–Mumford curve M. .
A characterization of the Artin–Mumford curve
KORCHMAROS, Gabor
2015-01-01
Abstract
Let M be the Artin–Mumford curve over the finite prime field Fp with p>2. By a result of Valentini and Madan, AutFp(M)≅H with H=(Cp×Cp)⋊Dp−1. We prove that if X is an algebraic curve of genus g=(p−1)2 defined over Fp such that AutFp(X) contains a subgroup isomorphic to H then X is birationally equivalent over Fp to the Artin–Mumford curve M. .File in questo prodotto:
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