2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72583In this paper we describe six pencils of K3-surfaces which have large Picard-Number and contain precisely five singular fibers: four have A-D-E singularities and one is non-reduced. In particular we describe these surfaces as cyclic coverings of the K3-surfaces which Barth and the author described in a previous manuscript (Asian. J. of Math. Vol. 7, No. 4, 519-538, Dec. 2003). In many cases using this description and lattice-Theory we are able to compute the exact Picard-number and to describe explicitly the Picard-lattices.21 pagesAlgebraic Geometry14J28;14L30;14E20;14C22text