Displaying similar documents to “On algebraic curves (of low genus) defined by Kleinian groups”

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.

Subvarieties of the Hyperelliptic Moduli Determined by Group Actions

Shaska, T. (2006)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 14Q05, 14Q15, 14R20, 14D22. Let Hg be the moduli space of genus g hyperelliptic curves. In this note, we study the locus Hg (G,σ) in Hg of curves admitting a G-action of given ramification type σ and inclusions between such loci. For each genus we determine the list of all possible groups, the inclusions among the loci, and the corresponding equations of the generic curve in Hg (G, σ). The proof of the results is based solely on representations...