I‑AIMS Institute for Artificial Intelligence
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On automorphisms of algebraic curves

S. Allen Broughton, Tanush Shaska, Aaron Wootton

I-AIMS paper 2018-6 · Published in Contemp. Math. 724 (2019), 175–212 · 2019

An irreducible, algebraic curve 𝒳_g of genus g ≥ 2 defined over an algebraically closed field k of characteristic char k = p ≥ 0, has finite automorphism group Aut(𝒳_g). In this paper we describe methods of determining the list of groups Aut(𝒳_g) for a fixed g ≥ 2. Moreover, equations of the corresponding families of curves are given when possible.

MSC classes: Primary 14H37; Secondary 30F10, 14H10, 14H45, 14H30, 14-02

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