On a Theorem of Castelnuovo, and the Equations Defining Space Curves.
L. Gruson, C. Peskine, R. Lazarsfeld (1983)
Inventiones mathematicae
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L. Gruson, C. Peskine, R. Lazarsfeld (1983)
Inventiones mathematicae
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Fabio Bardelli, Gian Pietro Pirola (1989)
Inventiones mathematicae
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A. Prabhakar Rao (1978/79)
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L. Chiantini, C. Ciliberto (1995)
Manuscripta mathematica
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Alan H. Durfee (1975)
Inventiones mathematicae
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Joe Harris (1980)
Mathematische Annalen
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E. Sernesi (1984)
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D.E. Rohrlich (1977)
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I. DOLGACEV (1969)
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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.