Rational Curves on K3 Surfaces

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.

12 pages, 1 figure, introduction rewritten and a figure added

Cited by in corpus (1)

• Density of Rational Curves on K3 Surfaces