Daigle, DanielMelle Hernández, Alejandro2023-06-202023-06-2020121609-3321https://hdl.handle.net/20.500.14352/43743Given 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 emptyengjournal articlehttp://www.ams.org/distribution/mmj/vol12-2-2012/daigle-melle-hernandez.pdfhttp://www.mathjournals.org/mmj/restricted access512.772rational curvesrational surfaceslinear systemsweighted cluster of singular pointsGeometria algebraica1201.01 Geometría Algebraica