Configurations de coniques et surfaces avec un nombre de Picard maximum. (Configurations of conics and surfaces with maximal Picard number)
One constructs various examples of surfaces (elliptic, K3, Horikawa surfaces,...) with maximum Picard number by considering double coverings of \(P^ 1\times P^ 1\) ramified along curves of the form \(\sum \Gamma_{\sigma}+\sum P^ 1\times \lambda +\sum \mu \times P^ 1\) where \(\Gamma\) is the diagonal and \(\sigma\) runs through a finite subgroup of PGL(1) (here PGL(1) is identified with the linear system of curves of bidegree (1,1) on \(P^ 1\times P^ 1)\). One reobtains (with different constructions) some results due to \textit{U. Persson} [cf. Math. Ann. 259, 287-312 (1982; Zbl 0466.14010)].
scientific article; zbMATH DE number 3989536