Classification of extremal elliptic K3 surfaces and fundamental groups of open K3 surfaces
Algebraic Geometry
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0007171,
title = {Classification of extremal elliptic K3 surfaces and fundamental groups of open K3 surfaces},
author = {I. Shimada and D. -Q. Zhang},
journal= {arXiv preprint arXiv:math/0007171},
year = {2007}
}
Comments
25 pages, Nagoya Math. J. to appear