Rational Curves on K3 Surfaces

Published 16 Dec 2010 in math.AG | (1012.3777v2)

Abstract: 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.

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