Rational Curves on K3 Surfaces

Details Rational Curves on K3 Surfaces Rational Curves on K3 Surfaces

2010-12-16

arxiv.org/abs/1012.3777v2

Mathematics

Algebraic Geometry

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

Scientific paper

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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