Some loci in Teichmüller space for genus seven defined by vanishing thetanulls.
Robert D.M. Accola (1993)
Manuscripta mathematica
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Robert D.M. Accola (1993)
Manuscripta mathematica
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Schmutz Schaller, Paul (2000)
Annales Academiae Scientiarum Fennicae. 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...
Ahmed Lesfari (1999)
Publicacions Matemàtiques
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The article studies geometrically the Euler-Arnold equations associatedto geodesic flow on for a left invariant diagonal metric. Such metric were first introduced by Manakov [17] and extensively studied by Mishchenko-Fomenko [18] and Dikii [6]. An essential contribution into the integrability of this problem was also made by Adler-van Moerbeke [4] and Haine [8]. In this problem there are four invariants of the motion defining in C = Lie( ⊗ C) an affine Abelian surface as complete intersection...
R. Donagi (1987)
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...
David Singerman (1997)
Mathematica Slovaca
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Hein, Georg (1997)
Beiträge zur Algebra und Geometrie
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Mika Seppälä (1990)
Compositio Mathematica
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Schmutz Schaller, Paul (2000)
Annales Academiae Scientiarum Fennicae. 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.