Opuscula Mathematica (Jan 2009)

Topological classification of conformal actions on p-hyperelliptic and (q,n)-gonal Riemann surfaces

  • Ewa Tyszkowska

DOI
https://doi.org/10.7494/OpMath.2009.29.4.443
Journal volume & issue
Vol. 29, no. 4
pp. 443 – 452

Abstract

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A compact Riemann surface \(X\) of genus \(g \gt 1\) is said to be \(p\)-hyperelliptic if \(X\) admits a conformal involution \(\rho\) for which \(X / \rho\) has genus \(p\). A conformal automorphism \(\delta\) of prime order \(n\) such that \(X / \delta\) has genus \(q\) is called a \((q,n)\)-gonal automorphism. Here we study conformal actions on \(p\)-hyperelliptic Riemann surface with \((q,n)\)-gonal automorphism.

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