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Group Actions, Cyclic Coverings and Families of K3-Surfaces

Published online by Cambridge University Press:  20 November 2018

Alessandra Sarti
Alessandra Sarti*
Affiliation:
Fachbereich für Mathematik, Johannes Gutenberg-Universität, 55099 Mainz, Germany e-mail: sarti@mathematik.uni-mainz.de
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Abstract

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In this paper we describe six pencils of $K3$-surfaces which have large Picard number $\left( \rho =19,20 \right)$ and each contains precisely five special fibers: four have $\text{A-D-E}$ 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.

Keywords

14J2814L3014E2014C22
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 4 , 01 December 2006 , pp. 592 - 608
Copyright
Copyright © Canadian Mathematical Society 2006

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