%0 Journal Article %A Daigle, Daniel %A Melle Hernández, Alejandro %T Linear systems of rational curves on rational surfaces %D 2012 %@ 1609-3321 %U https://hdl.handle.net/20.500.14352/43743 %X 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 arational 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 %~