Projective models of K3 surfaces with an even set

Details Projective models of K3 surfaces with an even set Projective models of K3 surfaces with an even set

2006-11-07

arxiv.org/abs/math/0611182v1

Mathematics

Algebraic Geometry

32 pages

Scientific paper

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 carefull 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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