Linear systems of rational curves on rational surfaces

摘要

Given a curve C on a projective nonsingular rational surface S, over analgebraically closed field of characteristic zero, we are interested in the setOmega_C of linear systems Lambda on S satisfying C is in Lambda, dim Lambda >0, and the general member of Lambda is a rational curve. The main result of thepaper gives a complete description of Omega_C and, in particular, characterizesthe curves C for which Omega_C is non empty.