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On ovals on Riemann surfaces. (English) Zbl 1087.14507
Summary: We prove that $$k$$ $$(k\geq 9)$$ non-conjugate symmetries of a Riemann surface of genus $$g$$ have at most $$2g- 2+ 2r- 3(9- k)$$ ovals in total, where $$r$$ is the smallest positive integer for which $$k\leq 2^{r-1}$$. Furthermore, we prove that for arbitrary $$k\geq 9$$ this bound is sharp for infinitely many values of $$g$$.

##### MSC:
 14H55 Riemann surfaces; Weierstrass points; gap sequences 30F10 Compact Riemann surfaces and uniformization
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