Existence of a rational elliptic surface with a given Mordell-Weil lattice

DOI10.3792/pjaa.68.251zbMath0785.14012OpenAlexW2078574460MaRDI QIDQ2366799

Tetsuji Shioda

Publication date: 20 April 1994

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.68.251

zbMATH Keywords

elliptic surfacesMordell-Weil latticesheight pairingminimal height of a non-torsion point

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Rational points (14G05) Elliptic curves (14H52) Elliptic surfaces, elliptic or Calabi-Yau fibrations (14J27) Other nonalgebraically closed ground fields in algebraic geometry (14G27) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items (7)

The minimal height of Jacobian fibrations on \(K3\) surfaces ⋮ Geometric consistency of Manin's conjecture ⋮ Multiplicative excellent family of type \(E_6\) ⋮ Gröbner basis, Mordell-Weil lattices and deformation of singularities. I ⋮ Gröbner basis, Mordell-Weil lattices and deformation of singularities. II ⋮ Mordell-Weil lattice via string junctions. ⋮ There is no Enriques surface over the integers

Cites Work

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• Mordell-Weil lattices and Galois representation. III
• Configurations of Kodaira fibers on rational elliptic surfaces
• Persson's list of singular fibers for a rational elliptic surface
• The canonical height and integral points on elliptic curves
• Construction of elliptic curves with high rank via the invariants of the Weyl groups
• On Mordell-Weil Lattices of TypeD5

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