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Group Actions, Cyclic Coverings and Families of K3-Surfaces

  Published:2006-12-01
 Printed: Dec 2006
  • Alessandra Sarti
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Abstract

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.
MSC Classifications: 14J28, 14L30, 14E20, 14C22 show english descriptions $K3$ surfaces and Enriques surfaces
Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
Coverings [See also 14H30]
Picard groups
14J28 - $K3$ surfaces and Enriques surfaces
14L30 - Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
14E20 - Coverings [See also 14H30]
14C22 - Picard groups
 

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