Algebraic surfaces and hyperbolic geometry
arXiv:1008.3825
Abstract
This is a survey of the Kawamata-Morrison cone conjecture on the structure of Calabi-Yau varieties and more generally Calabi-Yau pairs. We discuss the proof of the cone conjecture for algebraic surfaces, with plenty of examples. We show that the automorphism group of a K3 surface need not be commensurable with an arithmetic group, which answers a question by Mazur.
19 pages, 2 figures; to appear in the MSRI volume on Classical Algebraic Geometry Today