Group Actions, Cyclic Coverings and Families of K3-Surfaces

Details Group Actions, Cyclic Coverings and Families of K3-Surfaces Group Actions, Cyclic Coverings and Families of K3-Surfaces

2004-09-22

arxiv.org/abs/math/0409419v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

In 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.

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