## Tsukuba Journal of Mathematics

### The automorphism group of a cyclic $p$-gonal curve

#### Abstract

Let $M$ be a cyclic $p$-gonal curve with a positive prime number $p$, and let $V$ be the automorphism of order $p$ satisfying $M/ \lt V) \simeq \bf{P}^{1}$. It is well-known that finite subgroups $H$ of $\operatorname{Aut}(\bf{P}^{1})$ are classified into five types. In this paper, we determine the defining equation of $M$ with $H \subset \operatorname{Aut}(M/ \lt V \gt)$ for each type of $H$, and we make a list of hyperelliptic curves of genus 2 and cyclic trigonal curves of genus 5, 7, 9 with $H = Aut(M/ \lt V \gt)$.

#### Article information

Source
Tsukuba J. Math., Volume 31, Number 1 (2007), 1-37.

Dates
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1496165113

Digital Object Identifier
doi:10.21099/tkbjm/1496165113

Mathematical Reviews number (MathSciNet)
MR2337118

#### Citation

Ishii, Naonori; Yoshida, Katsuaki. The automorphism group of a cyclic $p$-gonal curve. Tsukuba J. Math. 31 (2007), no. 1, 1--37. doi:10.21099/tkbjm/1496165113. https://projecteuclid.org/euclid.tkbjm/1496165113