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