On automorphisms of algebraic curves

Abstract

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

Automorphisms and the canonical ideal

“…If the genus g of the curve X is g ≥ 2 then the automorphism group G = Aut(X) of the curve X is finite. The theory of automorphisms of curves is an interesting object of study, see the surveys [3], [7] and the references therein.…”

Automorphisms of algebraic curves

“…For a non-singular complete algebraic curve X over an algebraically closed field of characteristic p ≥ 0, if the genus g of the curve X is g ≥ 2 then the automorphism group G = Aut(X) of the curve X is finite. For the theory of automorphisms of curves we refer to the survey articles [1], [8].…”

“…μεγαλύτερο ή ίσο του 2 τότε η ομάδα αυτομορφισμών G = Aut(X) της καμπύλης είναι πεπερασμένη. Στη θεωρία των αυτομορφισμών καμπυλών αναφέρονται οι επισκοπήσεις [1], [8].…”