A note on the cone conjecture for K3 surfaces in positive characteristic

Details A note on the cone conjecture for K3 surfaces in positive characteristic A note on the cone conjecture for K3 surfaces in positive characteristic

2011-02-16

arxiv.org/abs/1102.3377v3

Mathematics

Algebraic Geometry

9 pages, comments welcome at any time. For some reason v2 equalled v1; this v3 is what was supposed to be v2. Enjoy!

Scientific paper

We prove that, for a K3 surface in characteristic p > 2, the automorphism group acts on the nef cone with a rational polyhedral fundamental domain and on the nodal classes with finitely many orbits. As a consequence, for any non-negative integer g, there are only finitely many linear systems of irreducible curves on the surface of arithmetic genus g, up to the action of the automorphism group.

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