Constructing rational curves on K3 surfaces

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Abstract

We develop a mixed-characteristic version of the Mori-Mukai technique for producing rational curves on K3 surfaces. We reduce modulo p, produce rational curves on the resulting K3 surface over a finite field, and lift to characteristic zero. As an application, we prove that all complex K3 surfaces with Picard group generated by a class of degree two have an infinite number of rationalcurves.

Original languageEnglish (US)
Pages (from-to)535-550
Number of pages16
JournalDuke Mathematical Journal
Volume157
Issue number3
DOIs
StatePublished - Apr 15 2011

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ASJC Scopus subject areas

  • Mathematics(all)

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