Dyson's lemma for products of two curves of arbitrary genus.
Paul Vojta (1989)
Inventiones mathematicae
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Paul Vojta (1989)
Inventiones mathematicae
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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.
Yukihiro Uchida (2011)
Acta Arithmetica
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Dan Abramovich, Joe Harris (1991)
Compositio Mathematica
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Joe Harris (1980)
Mathematische Annalen
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David Eisenbud, Joe Harris (1989)
Annales scientifiques de l'École Normale Supérieure
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L. Chiantini, C. Ciliberto (1995)
Manuscripta mathematica
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David Eisenbud, Joe Harris (1992)
Compositio Mathematica
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Abel Castorena (2005)
Bollettino dell'Unione Matematica Italiana
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In the moduli space of curves of genus , , let be the locus of curves that do not satisfy the Gieseker-Petri theorem. In the genus seven case we show that is a divisor in .