## Nagoya Mathematical Journal

### Classification of extremal elliptic {$K3$} surfaces and fundamental groups of open {$K3$} surfaces

#### Abstract

We present a complete list of extremal elliptic $K3$ surfaces (Theorem 1.1). 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 (Proposition 4.1 and Theorem 4.3).

#### Article information

Source
Nagoya Math. J., Volume 161 (2001), 23-54.

Dates
First available in Project Euclid: 27 April 2005

https://projecteuclid.org/euclid.nmj/1114631551

Mathematical Reviews number (MathSciNet)
MR1820211

Zentralblatt MATH identifier
1064.14503

Subjects
Primary: 14J27: Elliptic surfaces
Secondary: 14J28: $K3$ surfaces and Enriques surfaces

#### Citation

Shimada, Ichiro; Zhang, De-Qi. Classification of extremal elliptic {$K3$} surfaces and fundamental groups of open {$K3$} surfaces. Nagoya Math. J. 161 (2001), 23--54. https://projecteuclid.org/euclid.nmj/1114631551

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