Linear systems of rational curves on rational surfaces

الأصل · EN

Given a curve C on a projective nonsingular rational surface S, over an algebraically closed field of characteristic zero, we are interested in the set OmegaC 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 the paper gives a complete description of OmegaC and, in particular, characterizes the curves C for which OmegaC is non empty.