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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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