Large automorphism groups of ordinary curves of even genus in odd characteristic

Abstract

Let be a (projective, nonsingular, geometrically irreducible) curve of even genus defined over an algebraically closed field K of odd characteristic p. If the p-rank equals then is ordinary. In this paper, we deal with large automorphism groups G of ordinary curves of even genus. We prove that The proof of our result is based on the classification of automorphism groups of curves of even genus in positive characteristic by Giulietti and Korchmáros. According to this classification, for the exceptional cases and we show that the classical Hurwitz bound holds, unless p = 3, and an example for the latter case being given by the modular curve X(11) in characteristic 3.