## Publicacions Matemàtiques

### On $p$-hyperellipticity of doubly symmetric Riemann surfaces

Ewa Kozłowska-Walania

#### Abstract

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.

#### Article information

Source
Publ. Mat., Volume 51, Number 2 (2007), 291-307.

Dates
First available in Project Euclid: 31 July 2007

https://projecteuclid.org/euclid.pm/1185912164

Mathematical Reviews number (MathSciNet)
MR2334792

Zentralblatt MATH identifier
1137.30012

Subjects
Primary: 30F
Secondary: 14H

#### Citation

Kozłowska-Walania, Ewa. On $p$-hyperellipticity of doubly symmetric Riemann surfaces. Publ. Mat. 51 (2007), no. 2, 291--307. https://projecteuclid.org/euclid.pm/1185912164

#### References

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• E. Bujalance and A. F. Costa, On symmetries of $p$-hyperelliptic Riemann surfaces, Math. Ann. 308(1) (1997), 31\Ndash45.
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