An observation on (-1)-curves on rational surfaces

Abstract

We give an effective iterative characterization of the classes of (smooth, rational) (-1)-curves on the blowup of the projective plane at general points. Such classes are characterized as having self-intersection -1, arithmetic genus 0, and intersecting every (-1)-curve of smaller degree nonnegatively.

6 pages. v2: correction to statement of Lemma 2.2; rest of paper unaffected