Group Actions, Cyclic Coverings and Families of K3-Surfaces
Algebraic Geometry
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0409419,
title = {Group Actions, Cyclic Coverings and Families of K3-Surfaces},
author = {Alessandra Sarti},
journal= {arXiv preprint arXiv:math/0409419},
year = {2007}
}
Comments
21 pages