Rational curves on K3 surfaces

By Jun Li, C. Liedtke. 2010

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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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c8110d6d01e6b00873c5aec902bb8a0ee44a33b1