Abstract :
Let G=left angle bracketfright-pointing angle bracket 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 image of periods defined to be the subset of proper divisors d of N such that, for some xset membership, variantS, x is fixed by fd but not by any smaller power of f. For an arbitrary subset image of proper divisors of N, there is always an associated action and, if image denotes the minimal genus for such an action, an algorithm is obtained here to determine image. Furthermore, a set image is determined for which image is maximal.
