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An elliptic surface of Mordell-Weil rank 8 over the rational numbers

Charles F. Schwartz (1994)

Journal de théorie des nombres de Bordeaux

Néron showed that an elliptic surface with rank 8 , and with base B = P 1 , and geometric genus = 0 , may be obtained by blowing up 9 points in the plane. In this paper, we obtain parameterizations of the coefficients of the Weierstrass equations of such elliptic surfaces, in terms of the 9 points. Manin also describes bases of the Mordell-Weil groups of these elliptic surfaces, in terms of the 9 points ; we observe that, relative to the Weierstrass form of the equation, Y 2 = X 3 + A X 2 + B X + C (with deg ( A ) 2 , deg ( B ) 4 , and deg ( C ) 6 ) a basis ( X 1 , Y 1 ) , , ( X 8 , Y 8 ) can be found...

Automorphism groups of rational elliptic surfaces with section and constant J-map

Tolga Karayayla (2014)

Open Mathematics

In this paper, the automorphism groups of relatively minimal rational elliptic surfaces with section which have constant J-maps are classified. The ground field is ℂ. The automorphism group of such a surface β: B → ℙ1, denoted by Au t(B), consists of all biholomorphic maps on the complex manifold B. The group Au t(B) is isomorphic to the semi-direct product MW(B) ⋊ Aut σ (B) of the Mordell-Weil groupMW(B) (the group of sections of B), and the subgroup Aut σ (B) of the automorphisms preserving a...

Elliptic K3 surfaces as dynamical models and their Hamiltonian monodromy

Daisuke Tarama (2012)

Open Mathematics

This note deals with Lagrangian fibrations of elliptic K3 surfaces and the associated Hamiltonian monodromy. The fibration is constructed through the Weierstraß normal form of elliptic surfaces. There is given an example of K3 dynamical models with the identity monodromy matrix around 12 elementary singular loci.

Elliptic sufaces with a nef line bundle of genus two.

Antonio Lanteri, Cristina Turrini (1998)

Collectanea Mathematica

Complex projective elliptic surfaces endowed with a numerically effective line bundle of arithmetic genus two are studied and partially classified. A key role is played by elliptic quasi-bundles, where some ideas developed by Serrano in order to study ample line bundles apply to this more general situation.

Étude des fibrations elliptiques d’une surface K 3

Titem Harrache, Odile Lecacheux (2011)

Journal de Théorie des Nombres de Bordeaux

On s’intéresse aux fibrations elliptiques d’une surface K 3 singulière en vue de construire des courbes elliptiques avec 7 - torsion et rang > 0 sur .

Holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces

Vasile Brînzănescu, Ruxandra Moraru (2005)

Annales de l’institut Fourier

In this paper, we consider the problem of determining which topological complex rank-2 vector bundles on non-Kähler elliptic surfaces admit holomorphic structures; in particular, we give necessary and sufficient conditions for the existence of holomorphic rank-2 vector bundles on non-{Kä}hler elliptic surfaces.

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