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

We present a complete list of extremal elliptic K 3 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 K 3 surface to be trivial (Proposition 4.1 and Theorem 4.3).