Non-conservative function fields of genus (p + 1) /2.
Karl Otto Stöhr (1990)
Manuscripta mathematica
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Karl Otto Stöhr (1990)
Manuscripta mathematica
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Arnaldo Garcia (1986)
Manuscripta mathematica
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Uwe Pflaum (1987)
Manuscripta mathematica
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Kenji Ueno, Y. Namikawa (1973)
Manuscripta mathematica
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Ewa Tyszkowska (2005)
Colloquium Mathematicae
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A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if X admits a conformal involution ϱ, called a p-hyperelliptic involution, for which X/ϱ is an orbifold of genus p. If in addition X admits a q-hypereliptic involution then we say that X is pq-hyperelliptic. We give a necessary and sufficient condition on p,q and g for existence of a pq-hyperelliptic Riemann surface of genus g. Moreover we give some conditions under which p- and q-hyperelliptic involutions of...
L. Chiantini, C. Ciliberto (1995)
Manuscripta mathematica
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Teruo Takeuchi (1982)
Manuscripta mathematica
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Irene Llerena (1994)
Forum mathematicum
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Ballico, E. (1996)
Beiträge zur Algebra und Geometrie
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David Singerman, Paul Watson (1997)
Revista Matemática de la Universidad Complutense de Madrid
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We say that a finite group G of automorphisms of a Riemann surface X is non-maximal in genus g if (i) G acts as a group of automorphisms of some compact Riemann surface Xg of genus g and (ii), for all such surfaces Xg , |Aut Xg| > |G|. In this paper we investigate the case where G is a cyclic group Cn of order n. If Cn acts on only finitely many surfaces of genus g, then we completely solve the problem of finding all such pairs (n,g).
Michel Matignon (1987)
Manuscripta mathematica
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Jürgen Rathmann (1989)
Mathematische Zeitschrift
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E. Mezzetti, K. Ranestad (1991)
Manuscripta mathematica
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E.V. Flynn (1995)
Manuscripta mathematica
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P. Sarnak, P. Buser (1994)
Inventiones mathematicae
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Ewa Kozłowska-Walania (2007)
Colloquium Mathematicae
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We study the upper bounds for the total number of ovals of two symmetries of a Riemann surface of genus g, whose product has order n. We show that the natural bound coming from Bujalance, Costa, Singerman and Natanzon's original results is attained for arbitrary even n, and in case of n odd, there is a sharper bound, which is attained. We also prove that two (M-q)- and (M-q')-symmetries of a Riemann surface X of genus g commute for g ≥ q+q'+1 (by (M-q)-symmetry we understand a symmetry...