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Mathematical Research Letters
Volume 25 (2018)
A note on the cone conjecture for K3 surfaces in positive characteristic
Pages: 1879 – 1891
We prove that, for a $K3$ surface in characteristic $p \gt 2$, 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.
Received 1 August 2017
Published 25 March 2019