Geometric uniformization in genus 2.
Kuusalo, T., Näätänen, M. (1995)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Kuusalo, T., Näätänen, M. (1995)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Grzegorz Gromadzki (2000)
Revista Matemática Iberoamericana
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We prove that k (k ≥ 9) non-conjugate symmetries of a Riemann surface of genus g have at most 2g - 2 + 2(9 - k) ovals in total, where r is the smallest positive integer for which k ≤ 2. Furthermore we prove that for arbitrary k ≥ 9 this bound is sharp for infinitely many values of g.
Grzegorz Gromadzki (1990)
Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales
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Costa, Antonio F., Izquierdo, Milagros (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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Adnan Melekoglu (2000)
Revista Matemática Complutense
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Let X be a compact Riemmann surface of genus g > 1. A symmetry T of X is an anticonformal involution. The fixed point set of T is a disjoint union of simple closed curves, each of which is called a mirror of T. If T fixes g +1 mirrors then it is called an M-symmetry and X is called an M-surface. If X admits an automorphism of order g + 1 which cyclically permutes the mirrors of T then we shall call X an M-surface with the M-property. In this paper we investigate those M-surfaces...
G. Gromadzki, W. Marzantowicz (2011)
Fundamenta Mathematicae
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It is a natural question what is the set of minimal periods of a holomorphic maps on a Riemann surface of negative Euler characteristic. Sierakowski studied ordinary holomorphic periods on classical Riemann surfaces. Here we study orientation reversing automorphisms acting on classical Riemann surfaces, and also automorphisms of non-orientable unbordered Klein surfaces to which, following Singerman, we shall refer to as non-orientable Riemann surfaces. We get a complete set of conditions...
Bujalance, J.A., Estrada, B. (2002)
International Journal of Mathematics and Mathematical Sciences
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Rubén A. Hidalgo (2011)
Fundamenta Mathematicae
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Let S be a compact Klein surface together with a di-analytic involution κ: S → S. The lowest uniformizations of S are those whose deck group is an extended-Schottky group, that is, an extended Kleinian group whose orientation preserving half is a Schottky group. If S is a bordered compact Klein surface, then it is well known that κ can be lifted with respect to a suitable extended-Schottky uniformization of S. In this paper, we complete the above lifting property by proving that if S...
Arés Gastesi, Pablo (1999)
Annales Academiae Scientiarum Fennicae. Mathematica
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Helena B. Campos (2007)
RACSAM
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A closed (compact without boundary) Riemann surface S of genus g is said to be trigonal if there is a three sheeted covering (a trigonal morphism) from S to the Riemann sphere, ƒ : S →Ĉ. If there is an automorphism of period three, φ, on S permuting the sheets of the covering, we shall call S cyclic trigonal and will be called trigonal automorphism. In this paper we determine the intersection matrix on the first homology group of a cyclic trigonal Riemann surface on an adapted basis...
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...
Fuertes, Yolanda, González-Diez, Gabino (2003)
Annales Academiae Scientiarum Fennicae. Mathematica
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Robert Brooks (1998-1999)
Séminaire de théorie spectrale et géométrie
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