Even Sets of Eight Rational Curves on a K3-surface

Wolf Barth ()
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Wolf Barth: Mathematisches Institut der Universität

A chapter in Complex Geometry, 2002, pp 1-25 from Springer

Abstract: Abstract The aim of this note is to characterize in geometric terms the property that eight disjoint, smooth rational curves L i on a K3-surface Y form an even set, i.e. that their class Σ8 1[L i ] ∈ NS (X) is divisible by two. This is done for algebraic K3-surfaces arising in one of the following six (most elementary) ways: 1. double plane branched over a sextic curve with eight nodes; 2. double plane branched over a sextic curve with eight triple tangents; 3. quartic surface with eight nodes; 4. quartic surface carrying eight skew lines; 5. double quadric branched over a type (4,4) curve with eight nodes; 6. double quadric branched over a type (4,4) curve with eight double tangents.

Keywords: 2000; Mathematics Subject Classification; 14J28 (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-56202-0_1

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DOI: 10.1007/978-3-642-56202-0_1

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