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On symmetries of \(p\)-hyperelliptic Riemann surfaces. (English) Zbl 0879.30024
Let \(X\) be a compact Riemann surface of genus \(g>1\). It is called \(p\)-hyperelliptic if it admits a conformal involution \(\Phi_p\) such that \(X/\Phi_p\) has genus \(p\). A symmetry of \(X\) is an anticonformal involution \(\Phi: X\to X\). The fixed point set \(F(\Phi)\) of \(\Phi\) consists of \(k\) disjoint Jordan curves with \(0\leq k\leq g+1\). The species of \(\Phi\) is \(\pm k\) according to whether \(X\backslash F(\Phi)\) has two or one component. In this work, the possible species of symmetries of \(p\)-hyperelliptic Riemann surfaces are studied for the general and various special cases.

30F10 Compact Riemann surfaces and uniformization
14H55 Riemann surfaces; Weierstrass points; gap sequences
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
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