Schottky uniformization theory on Riemann surfaces and Mumford curves of infinite genus.

Takashi Ichikawa

Displaying similar documents to “Schottky uniformization theory on Riemann surfaces and Mumford curves of infinite genus.”

On pq-hyperelliptic Riemann surfaces

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...

Geometric uniformization in genus 2.

Kuusalo, T., Näätänen, M. (1995)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

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On the connectedness of the locus of real Riemann surfaces.

Costa, Antonio F., Izquierdo, Milagros (2002)

Annales Academiae Scientiarum Fennicae. Mathematica

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Descent via (3,3)-isogeny on Jacobians of genus 2 curves

Nils Bruin, E. Victor Flynn, Damiano Testa (2014)

Acta Arithmetica

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We give a parametrization of curves C of genus 2 with a maximal isotropic (ℤ/3)² in J[3], where J is the Jacobian variety of C, and develop the theory required to perform descent via (3,3)-isogeny. We apply this to several examples, where it is shown that non-reducible Jacobians have non-trivial 3-part of the Tate-Shafarevich group.