RMC - Vol. 21 Num. 1 - Grzegorz Gromadzki

Full paper in PDF format:
$%G. Gromadzki, On conjugacy of p-gonal automorphisms of Riemann surfaces, Rev. Mat. Complut. 21 (2008), no. 1, 83–87.%$

On Conjugacy of p-gonal Automorphisms
of Riemann Surfaces

Grzegorz GROMADZKI

Institute of Mathematics
University of Gdańsk
Wita Stwosza 57
80-952 Gdańsk — Poland
greggrom@math.univ.gda.pl

Received: January 8, 2007
Accepted: August 30, 2007

ABSTRACT

The classical Castelnuovo-Severi theorem implies that for $2 g > (p - 1)$ , a $p$ -gonal automorphism group of a cyclic $p$ -gonal Riemann surface $X$ of genus $g$ is unique. Here we deal with the case $2 g ≤ (p- 1)$ ; we give a new and short proof of a result of González-Diez that a cyclic $p$ -gonal Riemann surface of such genus has one conjugacy class of $p$ -gonal automorphism groups in the group of automorphisms of $X$ .

Key words: automorphisms of Riemann surfaces, fixed points, ramified coverings of Riemann surfaces, hyperellipticity.
2000 Mathematics Subject Classification: Primary 30F10; Secondary 14H37, 14H55.