Displaying similar documents to “Curves of genus g lying on a g-dimensional Jacobian variety.”

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.

Curves of genus seven that do not satisfy the Gieseker-Petri theorem

Abel Castorena (2005)

Bollettino dell'Unione Matematica Italiana

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In the moduli space of curves of genus g , g , let 𝒢𝒫 g be the locus of curves that do not satisfy the Gieseker-Petri theorem. In the genus seven case we show that 𝒢𝒫 7 is a divisor in 7 .