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

On Conjugacy of *p*-gonal Automorphisms

of Riemann Surfaces

of Riemann Surfaces

Grzegorz GROMADZKI

University of Gdańsk

Wita Stwosza 57

80-952 Gdańsk — Poland

greggrom@math.univ.gda.pl

Accepted: August 30, 2007

ABSTRACT

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

Key words: automorphisms of Riemann surfaces, fixed points, ramified coverings of
Riemann surfaces, hyperellipticity.

2000 Mathematics Subject Classification: Primary 30F10; Secondary 14H37, 14H55.