## Duke Mathematical Journal

### The cone conjecture for Calabi-Yau pairs in dimension 2

Burt Totaro

#### Abstract

We prove the Morrison-Kawamata cone conjecture for Kawamata log terminal Calabi-Yau pairs in dimension $2$. 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.

#### Article information

Source
Duke Math. J., Volume 154, Number 2 (2010), 241-263.

Dates
First available in Project Euclid: 16 August 2010

https://projecteuclid.org/euclid.dmj/1281963650

Digital Object Identifier
doi:10.1215/00127094-2010-039

Mathematical Reviews number (MathSciNet)
MR2682184

Zentralblatt MATH identifier
1203.14046

#### Citation

Totaro, Burt. The cone conjecture for Calabi-Yau pairs in dimension 2. Duke Math. J. 154 (2010), no. 2, 241--263. doi:10.1215/00127094-2010-039. https://projecteuclid.org/euclid.dmj/1281963650

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