Algebraic curves with a large cyclic automorphism group

Abstract

The study of algebraic curves with numerous automorphisms in relation to their genus is a well-established area in Algebraic Geometry. In 1995, Irokawa and Sasaki gave a complete classification of curves over the complex field with an automorphism of order at least 2g+1. Such a classification does not hold in positive characteristic p, the curve with equation y^2=x^p-x being a well-studied counterexample. This paper successfully classifies curves with a cyclic automorphism group of order at least 2g+1 in positive characteristic greater than 2 , offering the positive characteristic counterpart to the Irokawa-Sasaki result. The possibility of wild ramification in positive characteristic has presented a few challenges to the investigation