LINEAR-SYSTEMS OF PLANE-CURVES THROUGH FIXED FAT POINTS OF P2

Given any s points P1,..., Ps in P2 and s positive integers m1,..., ms, let Sn be the linear system of plane curves of degree n through Pi with multiplicity at least mi (1 ≤ i ≤ s). We give numerical bounds for the regularity of Sn in the following cases (a) the points Pi are non-singular points of an integral curve of degree d; (b) the Pi's are in general position; (c) the Pi's are in uniform position; (d) the Pi's are generic points of P2. We also study the sharpness of such bounds. © 1991.