Group Actions, Cyclic Coverings and Families of K3-Surfaces

Canadian mathematical bulletin

关键词: symmetric matrices;    eigenvalues;    elliptic surfaces;    K3 surfaces;    Néron--Severi group;    rational curves;    Diophantine equations;    arithmetic geometry;    algebraic geometry;    number theory;   

DOI  :  10.4153/CMB-2006-055-0

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper we describe six pencils of $K3$-surfaces which havelarge Picard number ($ho=19,20$) and each contains precisely fivespecial fibers: four have A-D-E singularities and one isnon-reduced. In particular, we characterize these surfaces as cycliccoverings of some $K3$-surfaces described in a recent paper by Barthand the author.In many cases, using3-divisible sets, resp., 2-divisible sets, of rational curves andlattice theory, we describe explicitly the Picard lattices.

【 授权许可】

Unknown