Big rational surfaces (Q637590)

The authors prove that the Cox ring of any smooth rational surface with big anticanonical class is finitely generated. This leads naturally to attempt a classification of big rational surfaces. The authors make a first step towards this goal by classifying blow-ups of \(\mathbb P^2\) at finite sets of points for which the anticanonical class is both big and effective. They put their result in perspective with respect to several recent results in the literature.