Sets of periods for automorphisms of compact Riemann surfaces

Let G = < f > be a finite cyclic group of order N that acts by conformal automorphisms on a compact Riemann surface S of genus g >= 2. Associated to this is a set A of periods defined to be the subset of proper divisors d of N such that, for some x is an element of S, x is fixed by f(d) but not by any smaller power of f. For an arbitrary subset A of proper divisors of N, there is always an associated action and, if g(A) denotes the minimal genus for such an action, an algorithm is obtained here to determine g(A). Furthermore, a set A(max) is determined for which g(A) is maximal. (c) 2006 Elsevier B.V. All rights reserved.