Open Access
2013 On the ample cone of a rational surface with an anticanonical cycle
Robert Friedman
Algebra Number Theory 7(6): 1481-1504 (2013). DOI: 10.2140/ant.2013.7.1481


Let Y be a smooth rational surface, and let D be a cycle of rational curves on Y that is an anticanonical divisor, i.e., an element of |KY|. Looijenga studied the geometry of such surfaces Y in case D has at most five components and identified a geometrically significant subset R of the divisor classes of square 2 orthogonal to the components of D. Motivated by recent work of Gross, Hacking, and Keel on the global Torelli theorem for pairs (Y,D), we attempt to generalize some of Looijenga’s results in case D has more than five components. In particular, given an integral isometry f of H2(Y) that preserves the classes of the components of D, we investigate the relationship between the condition that f preserves the “generic” ample cone of Y and the condition that f preserves the set R.


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Robert Friedman. "On the ample cone of a rational surface with an anticanonical cycle." Algebra Number Theory 7 (6) 1481 - 1504, 2013.


Received: 2 August 2012; Revised: 27 November 2012; Accepted: 3 January 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 06226676
MathSciNet: MR3107570
Digital Object Identifier: 10.2140/ant.2013.7.1481

Primary: 14J26

Keywords: ample cone , anticanonical cycle , exceptional curve , rational surface

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 6 • 2013
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