Rational curves on K3 surfaces

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24 Scopus citations


We show that projective K3 surfaces with odd Picard rank contain infinitely many rational curves. Our proof extends the Bogomolov-Hassett-Tschinkel approach, i.e., uses moduli spaces of stable maps and reduction to positive characteristic.

Original languageEnglish
Pages (from-to)713-727
Number of pages15
JournalInventiones Mathematicae
Issue number3
StatePublished - Jun 2012
Externally publishedYes


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