Let p be an odd prime. We study the Artin-Schreier analogue of Poonen's problem of constructing curves without extra automorphisms. An Artin-Schreier curve carries an unavoidable deck group Cp, so the smallest possible full geometric automorphism group inside the Artin-Schreier locus is Cp. We determine the exact numer...
Let X be a smooth projective curve of genus g>= 2 over an algebraically closed field K, and suppose that Aut(X) contains a cyclic subgroup G of order N>2g - 2. The cases N>= 2g + 1 are known. We treat the two boundary values N = 2g and N = 2g - 1. In the tame case we obtain an explicit finite list of ramification signa...
Let p be an odd prime, let q_0 := p^s with s>= 1, and put q := p q_0^2. We study the smooth projective curve R_{p,s} with function field F_q(x,y,z), y^q - y = x^{q_0}(x^q - x), z^q - z = x^{2q_0}(x^q - x). The two-equation layer is already present in the ray-class and big-action literature; for p = 3 it gives the class...
A. Kazemifard, Saeed Tafazolian· 0 citations
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