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On hyperellipticity degree of bisymmetric Riemann surfaces admitting a fixed point free symmetry
by Ewa koz lowska-walania

Vol. 5 No. 4 (2010) P.457~P.468

ABSTRACT

We study pairs of commuting symmetries of a Riemann surface of genus $g\geq 2$, assuming that one of them is fixed point free. We find necessary and sufficient conditions for an integer $p$ to be the degree of hyperellipticity of their product, being given the number of ovals and separabilities of the symmetries. In the last part of the paper, using well known formula on the number $m$ of points fixed by the conformal involution of a Riemann surface, we find all possible values of $m$ that can be attained for the product of our symmetries.

KEYWORDS
Riemann surface, symmetry of Riemann surface, oval of a symmetry of a Riemann surface

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 30F50, 14H37

MILESTONES