Classification of extremal elliptic K3 surfaces and fundamental groups of open K3 surfaces

Details Classification of extremal elliptic K3 surfaces and fundamental groups of open K3 surfaces Classification of extremal elliptic K3 surfaces and fundamental groups of open K3 surfaces

2000-07-27

arxiv.org/abs/math/0007171v1

Mathematics

Algebraic Geometry

25 pages, Nagoya Math. J. to appear

Scientific paper

We present a complete list of extremal elliptic K3 surfaces. There are altogether 325 of them. The first 112 coincides with Miranda-Persson's list for semi-stable ones. The data include the transcendental lattice which determines uniquely the K3 surface by a result of Shioda and Inose, the singular fibre type and the Mordell Weil group. As an application, we give a sufficient condition for the topological fundamental group of complement to an ADE-configuration of smooth rational curves on a K3 surface to be trivial.

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