Mathematical Research Letters

Volume 25 (2018)

Number 6

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

Pages: 1879 – 1891



Max Lieblich (Department of Mathematics, University of Washington, Seattle, Wa., U.S.A.)

Davesh Maulik (Massachusetts Institute of Technology, Cambridge, Massachusetts, U.S.A.)


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

Accepted 30 January 2018

Published 25 March 2019