English

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.

Keywords

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

R2 v1 2026-06-21T17:27:25.236Z