Sets of periods for automorphisms of compact Riemann surfaces |
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Authors: | Micha? Sierakowski |
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Institution: | Information Technology Centre PKO BP SA, Wólczyńska 133, 00-975 Warsaw, Poland |
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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 fd 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 gA denotes the minimal genus for such an action, an algorithm is obtained here to determine gA. Furthermore, a set Amax is determined for which gA is maximal. |
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Keywords: | 30F10 30F35 37E30 |
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