Regularity of linear systems of plane curves

Abstract

The subject of this paper is the study of linear systems of plane curves which are given by assigning a set of fixed multiple points. This study not only has an interest per se, but is connected to other subjects (for example, results on rational surfaces and curves on them can be found in [Ro], [A], and [Gil). A linear system of plane curves of (projective) dimension r is a subvector space I, s