Extremal elliptic fibrations and singular \(K3\) surfaces (Q1970884)

In this paper one considers relatively minimal fibrations \(f:X\to \mathbb{P}^1\) having a section, over an algebraically closed field of any characteristic. Firstly one recovers the classification done by \textit{U. Schmickler-Hirzebruch} [``Elliptische Flächen über \(\mathbb{P}^1\mathbb{C}\) mit drei Ausnahmefasern und die hypergeometrische Differentialgleichung'', Schriftenr. Math. Inst. Univ. Münster, n. Ser. 33 (1985; Zbl 0589.14011)] for non-trivial fibrations with at most three singular fibres in characteristic zero. Then one addresses the natural question ``For which characteristics defines the Weierstrass equation a supersingular K3 surface?'' In this respect the main result is theorem 3.4.