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Oberseminar WiSe 2010/11 Zusammenfassung des Vortrags von Arthur Prendergast-Smith

The cone conjecture for abelian varieties

The cone conjecture of Morrison and Kawamata predicts that the nef cone of a projective variety should be rational polyhedral up to automorphisms, in various Calabi–Yau-type situations. I will discuss a proof of the conjecture in the case of abelian varieties. The key ingredient is reduction theory for arithmetic group actions on homogeneous cones, due to Ash.