Algebraic surfaces and hyperbolic geometry

Mathematics – Algebraic Geometry

Scientific paper

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19 pages, 2 figures; to appear in the MSRI volume on Classical Algebraic Geometry Today

Scientific paper

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.

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