On large automorphism groups of algebraic curves in positive characteristic

Giulietti, Massimo; Korchmaros, Gabor

On large automorphism groups of algebraic curves in positive characteristic

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In his investigation on large $K$-automorphism groups of an algebraic curve, Stichtenoth obtained an upper bound on the order of the first ramification group of an algebraic curve $\cX$ defined over an algebraically closed field of characteristic $p$. Stichtenoth's bound has raised the problem of classifying all $\K$-automorphism groups $G$ of $\cX$ with the following property: There is a point $P\in \cX$ for which \begin{equation} |G_P^{(1)}|>\frac{p}{p-1}g. \end{equation} Such a classification is obtained here by proving Theorem 1.3