Elliptic fibrations of some extremal K3 surfaces

Details Elliptic fibrations of some extremal K3 surfaces Elliptic fibrations of some extremal K3 surfaces

2004-12-02

arxiv.org/abs/math/0412049v3

Mathematics

Algebraic Geometry

27 pages, 33 figures, 2 tables; major revision: Third version has minor typos corrected, exposition improved and references up

Scientific paper

This paper is concerned with the construction of extremal elliptic K3 surfaces. It gives a complete treatment of those fibrations which can be derived from rational elliptic surfaces by easy manipulations of their Weierstrass equations. In particular, this approach enables us to find explicit equations for 38 semi-stable extremal elliptic K3 fibrations, 32 of which are indeed defined over the rationals. They are realized as pull-back of non-semi-stable extremal rational elliptic surfaces via base change. This is related to work of J. Top and N. Yui which exhibited the same procedure for the semi-stable extremal rational elliptic surfaces.

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