Linear systems of rational curves on rational surfaces

Abstract

Given a curve C on a projective nonsingular rational surface S, over an algebraically closed eld of characteristic zero, we are interested in the set C of linear systems L on S satisfying C 2 L, dimL 1, and the general member of L is a rational curve. The main result of the paper gives a complete description of C and, in particular, characterizes the curves C for which C is non empty