Geodesic
Group Actions, Cyclic Coverings and Families of K3-Surfaces
Canadian mathematical bulletin, Tome 49 (2006) no. 4, pp. 592-608

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DOI

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.
DOI : 10.4153/CMB-2006-055-0
Mots-clés : 14J28, 14L30, 14E20, 14C22 
Sarti, Alessandra. Group Actions, Cyclic Coverings and Families of K3-Surfaces. Canadian mathematical bulletin, Tome 49 (2006) no. 4, pp. 592-608. doi: 10.4153/CMB-2006-055-0
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     title = {Group {Actions,} {Cyclic} {Coverings} and {Families} of {K3-Surfaces}},
     journal = {Canadian mathematical bulletin},
     pages = {592--608},
     year = {2006},
     volume = {49},
     number = {4},
     doi = {10.4153/CMB-2006-055-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-055-0/}
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