The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a careful analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate their relation with K3 surfaces with a Nikulin involution.
Projective models of $K3$ surfaces with an even set / A. Garbagnati, A. Sarti. - In: ADVANCES IN GEOMETRY. - ISSN 1615-715X. - 8:3(2008), pp. 413-440.
Projective models of $K3$ surfaces with an even set
A. GarbagnatiPrimo
;
2008
Abstract
The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a careful analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate their relation with K3 surfaces with a Nikulin involution.
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