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Constructing rational curves on K3 surfaces
"... Abstract. We develop a mixedcharacteristic version of the MoriMukai 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 ..."
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Abstract. We develop a mixedcharacteristic version of the MoriMukai 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 rational curves. Contents