On certain elliptic surfaces with maximal Picard number (Q1064373)

The paper classifies elliptic fibrations \(f: X\to B\) for which (1) the Picard number N of X is maximal, i.e. equal to the Hodge number \(h^{1,1}\) and (2) the rank of the divisor class group of the generic fibre of f is zero. In this classification one naturally encounters Shioda's elliptic modular surfaces [cf. \textit{T. Shioda}, J. Math. Soc. Japan 24, 20-59 (1972; Zbl 0226.14013)] and a slight generalisation of them called by the author ''generalised elliptic modular surfaces''. The latter surfaces are constructed starting from subgroups of finite index in \(PSL_ 2({\mathbb{Z}})\).