We prove the Morrison-Kawamata cone conjecture for Kawamata log terminal Calabi-Yau pairs in dimension . For a large class of rational surfaces as well as for K3 surfaces and abelian surfaces, the action of the automorphism group of the surface on the convex cone of ample divisors has a rational polyhedral fundamental domain.
"The cone conjecture for Calabi-Yau pairs in dimension 2." Duke Math. J. 154 (2) 241 - 263, 15 August 2010. https://doi.org/10.1215/00127094-2010-039