Constructing rational curves on K3 surfaces

Details Constructing rational curves on K3 surfaces Constructing rational curves on K3 surfaces

2009-07-21

arxiv.org/abs/0907.3527v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

We develop a mixed-characteristic version of the Mori-Mukai 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.

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