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2007 On $p$-hyperellipticity of doubly symmetric Riemann surfaces
Ewa Kozłowska-Walania
Publ. Mat. 51(2): 291-307 (2007).


Studying commuting symmetries of $p$-hyperelliptic Riemann surfaces, Bujalance and Costa found in "On symmetries of $p$-hyperelliptic Riemann surfaces" (E. Bujalalance, A.F. Costa, Math. Ann. 308(1) (1997), 31–45) upper bounds for the degree of hyperellipticity of the product of commuting $(M-q)$- and $(M-q')$-symmetries, depending on their separabilities. Here, we find necessary and sufficient conditions for an integer $p$ to be the degree of hyperellipticity of the product of two such symmetries, taking into account their separabilities. We also give some results concerning the existence and uniqueness of symmetries from which we obtain a series of important results of Natanzon concerning $M$- and $(M-1)$-symmetries.


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Ewa Kozłowska-Walania. "On $p$-hyperellipticity of doubly symmetric Riemann surfaces." Publ. Mat. 51 (2) 291 - 307, 2007.


Published: 2007
First available in Project Euclid: 31 July 2007

zbMATH: 1137.30012
MathSciNet: MR2334792

Primary: 30F
Secondary: 14H

Keywords: oval of a symmetry of a Riemann surface , Riemann surface , symmetry of Riemann surface

Rights: Copyright © 2007 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.51 • No. 2 • 2007
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