Maps of linear systems on blow-ups of the projective plane

Let X be the blow-up of P-2 at n points p(1),...,p(n) in linearly general p osition, let F be a numerically effective divisor on X, and let L be the to tal transform on X of a line on P-2. The natural multiplication map Gamma ( X, O-X(F)) x Gamma (X, O-X(L)) --> Gamma (X, O-X(F + L)) is shown to be sur jective for a particular subset of numerically effective divisors. This res ult implicitly determines minimal free resolutions of ideals defining fat p oint subschemes supported at six or fewer general points of P-2. All work i s over an algebraically closed field k. (C) 2001 Elsevier Science B.V. All rights reserved. MSC: 14; 13.