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 .
"On the ample cone of a rational surface with an anticanonical cycle." Algebra Number Theory 7 (6) 1481 - 1504, 2013. https://doi.org/10.2140/ant.2013.7.1481