Real Algebraic and Analytic Geometry |

On the number of ovals of a symmetry of a compact Riemann surface.

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Submission: 2005, January 14.

*Abstract:
Let X be a symmetric compact Riemann surface whose
full group of conformal automorphisms is cyclic. We derive a formula
for counting the number of ovals of the symmetries of X in terms of
surprisingly few data of the monodromy of the covering of X over X/G,
where G is the full group of conformal and anticonformal automorphisms of X.*

Mathematics Subject Classification (2000): 30F, 14H.

Keywords and Phrases: Riemann surface, symmetries, ovals.

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