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Let X be a compact Riemann surface of genus g > 1. A symmetry S of X is an anticonformal involution. We write jSj for the number of connected components of the xed points set of S. Suppose that X admits two distinct symmetries S 1 and S 2 ; then we nd a bound for jS 1 j + jS 2 j in terms of the genus of X and the order of S 1 S 2. We discuss circumstances(More)
This paper explains some facts probably known to experts and implicitely contained in the literature about dessins d'enfants but which seem to be nowhere explicitely stated. The 1-skeleton of every regular Cori hypermap is the Cayley graph of its automorphism group, embedded in the underlying orientable surface. Conversely, every Cayley graph of a finite(More)
Macbeath gave a formula for the number of fixed points for each non-identity element of a cyclic group of automorphisms of a compact Riemann surface in terms of the universal covering transformation group of the cyclic group. We observe that this formula generalizes to determine the fixed-point set of each non-identity element of a cyclic group of(More)