1. CMB 2006 (vol 49 pp. 592)
|Group Actions, Cyclic Coverings and Families of K3-Surfaces |
In this paper we describe six pencils of $K3$-surfaces which have large Picard number ($\rho=19,20$) and each contains precisely five special fibers: four have A-D-E singularities and one is non-reduced. In particular, we characterize these surfaces as cyclic coverings of some $K3$-surfaces described in a recent paper by Barth and the author. In many cases, using 3-divisible sets, resp., 2-divisible sets, of rational curves and lattice theory, we describe explicitly the Picard lattices.
Categories:14J28, 14L30, 14E20, 14C22