Abstract

We give necessary and suficient conditions for a divisor class on smooth projective anticanonical rational surfaces to be the class of a smooth rational curve of self-intersection −1. We characterize smooth projective anticanonical rational surfaces for which the monoid of classes (modulo algebraic equivalence) of effective divisors is not finitely generated, extending results of Lahyane for the case of rational surfaces X with K_X² = 0.

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