Revista Matemática Iberoamericana

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Volume 16, Issue 3, 2000, pp. 515–527
DOI: 10.4171/RMI/282

Published online: 2000-12-31

On ovals on Riemann surfaces

Grzegorz Gromadzki[1]

(1) University of Gdańsk, Poland

We prove that $k (k ≥ 9)$ non-conjugate symmetries of a Riemann surface of genus $g$ have at most $2g-2+2^{r-3}(9-k)$ ovals in total, where $r$ is the smallest positive integer for which $k≤2^{r-1}$. Furthermore we prove that for arbitrary $k≥9$ this bound is sharp for infinitely many values of $g$.

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Gromadzki Grzegorz: On ovals on Riemann surfaces. Rev. Mat. Iberoam. 16 (2000), 515-527. doi: 10.4171/RMI/282