Abstract
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 ∈ 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.
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