Elliptic curves on Abelian surfaces.
Ernst Kani (1994)
Manuscripta mathematica
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Ernst Kani (1994)
Manuscripta mathematica
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Eyal Z. Goren (1997)
Manuscripta mathematica
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Josep González, Jordi Guàrdia, Victor Rotger (2005)
Acta Arithmetica
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Keil, Mitchel J., Rodriguez, Jorge (1999)
Journal for Geometry and Graphics
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Frans Oort (1975)
Mathematische Annalen
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Tomasz Lenarcik (2011)
Annales Polonici Mathematici
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We propose a combinatorial method of proving non-specialty of a linear system of curves with multiple points in general position. As an application, we obtain a classification of special linear systems on ℙ¹×ℙ¹ with multiplicities not exceeding 3.
Tomasz Szemberg (1996)
Annales Polonici Mathematici
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Principally polarized abelian surfaces are the Jacobians of smooth genus 2 curves or of stable genus 2 curves of special type. In [S] we studied equations describing Kummer surfaces in the case of an irreducible principal polarization on the abelian surface. The aim of this note is to give a treatment of the second case. We describe intermediate Kummer surfaces coming from abelian surfaces carrying a product principal polarization. In Proposition 12 we give explicit equations of these...
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.
Gert-Martin Greuel, Christoph Lossen (1996)
Manuscripta mathematica
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Andrew Bremner (1991)
Manuscripta mathematica
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Keisuke Arai (2014)
Acta Arithmetica
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In previous articles, we showed that for number fields in a certain large class, there are at most elliptic points on a Shimura curve of Γ₀(p)-type for every sufficiently large prime number p. In this article, we obtain an effective bound for such p.
Kenji Ueno, Y. Namikawa (1973)
Manuscripta mathematica
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Bernd Jakob (1994)
Manuscripta mathematica
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L. Chiantini, C. Ciliberto (1995)
Manuscripta mathematica
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Fumio Sakai (1987)
Manuscripta mathematica
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Allen Tannenbaum (1982)
Mathematische Annalen
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Ingrid Bauer (1995)
Manuscripta mathematica
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