Algebra & Number Theory
- Algebra Number Theory
- Volume 7, Number 6 (2013), 1481-1504.
On the ample cone of a rational surface with an anticanonical cycle
Let be a smooth rational surface, and let be a cycle of rational curves on that is an anticanonical divisor, i.e., an element of . Looijenga studied the geometry of such surfaces in case has at most five components and identified a geometrically significant subset of the divisor classes of square orthogonal to the components of . Motivated by recent work of Gross, Hacking, and Keel on the global Torelli theorem for pairs , we attempt to generalize some of Looijenga’s results in case has more than five components. In particular, given an integral isometry of that preserves the classes of the components of , we investigate the relationship between the condition that preserves the “generic” ample cone of and the condition that preserves the set .
Algebra Number Theory, Volume 7, Number 6 (2013), 1481-1504.
Received: 2 August 2012
Revised: 27 November 2012
Accepted: 3 January 2013
First available in Project Euclid: 20 December 2017
Permanent link to this document
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14J26: Rational and ruled surfaces
Friedman, Robert. On the ample cone of a rational surface with an anticanonical cycle. Algebra Number Theory 7 (2013), no. 6, 1481--1504. doi:10.2140/ant.2013.7.1481. https://projecteuclid.org/euclid.ant/1513730035