A note on the cone conjecture for K3 surfaces in positive characteristic
Algebraic Geometry
2019-10-30 v7 Number Theory
Abstract
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.
Cite
@article{arxiv.1102.3377,
title = {A note on the cone conjecture for K3 surfaces in positive characteristic},
author = {Max Lieblich and Davesh Maulik},
journal= {arXiv preprint arXiv:1102.3377},
year = {2019}
}
Comments
9 pages, comments welcome at any time. Correction to the statement of Theorem 2.1 and the authors' email addresses