On symmetries of pq-hyperelliptic Riemann surfaces
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Tyszkowska, Ewa [1]
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[1] University of Gdańsk
University of Gdańsk
Gdańsk, Polonia
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- Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 25, Nº. 2, 2006, págs. 179-189
- Idioma: inglés
- DOI: 10.4067/S0716-09172006000200004
- Enlaces
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Resumen
A symmetry of a Riemann surface X is an antiholomorphic involution φ. The species of φ is the integer εk, where k is the number of connected components in the set Fix(φ) of fixed points of φ and ε = -1 if X \ Fix(φ) is connected and ε = 1 otherwise. A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if it admits a conformal involution ρ, called a p-hyperelliptic involution, for which X/ρ is an orbifold of genus p. Symmetries of p-hyperelliptic Riemann surfaces has been studied by Klein for p = 0 and by Bujalance and Costa for p > 0. Here we study the species of symmetries of so called pq-hyperelliptic surface defined as a Riemann surface which is p- and q-hyperelliptic simultaneously
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Referencias bibliográficas
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- [2] E. Bujalance, A.F.Costa: ”On symmetries of p-hyperelliptic Riemann surfaces”, Springer-Verlag (1997),
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- [4] A.Harnack: ”Uber die Vieltheiligkeit der ebenen algebraischen Kurven”, Math. Ann. 10, (1876), pp. 189-199.
- [5] F.Klein: Uber Realitätsverhältnisse bei einem beliebigen Geschlechte zugehörigen Normalkurve der ϕ” Math. Ann. 42 (1893) 1-29.
- [6] A. M. Macbeath: "Action of automorphisms of a compact Riemann surface on the first homology group". Bull. London Math. Soc. 5...
- [7] E. Tyszkowska, On pq-hyperelliptic Riemann surfaces, Coll. Math. 103 (1), (2005), 115-120.
- [8] E. Tyszkowska, On p-hyperelliptic involutions of Riemann surfaces, Beiträge zur Algebra und Geometrie, to appear.
