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

2000/07/27 by Ichiro Shimada, I. Shimada, Shimada, I. +3 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Finite Group Theory Research #math.AG #msc:14E20 #msc:14J28

paper · pdf · doi:10.48550/arxiv.math/0007171

25 pages, Nagoya Math. J. to appear

arxiv created 2000/07/27 · arxiv updated 2009/11/30

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.

Cited by

• The Arithmetic Geometry of Square-Sided Heron Triangles
• Monodromies of rational elliptic surfaces and extremal elliptic K3 surfaces

Related

• On Extremal Elliptic K3 Surfaces
• Elliptic fibrations of some extremal K3 surfaces
• Monodromies of rational elliptic surfaces and extremal elliptic K3 surfaces
• On elliptic K3 surfaces
• Classifications of elliptic fibrations of a singular K3 surface