ABSTRACT
This chapter deals with a paper which is intended as a tribute to the outstanding algebraic geometers F. Enriques and B. Segre, who have been working for many years at the University of Bologna. It consists in a survey report on some recent results on linear systems of plane curves inspired by or related with a minor but interesting part of their work, and shows how one can find plenty of ideas also in little things. Our starting points are two theorems of B. Segre, one relating complete intersections and postulation, and the other dealing with regularity of linear systems; and one by Enriques on projections of space curves. Fortunately these results, besides some pretty ideas, contain some obscure points. The chapter discusses the above-mentioned results, and gives a few related results taken from some papers either in print, or in preparation, trying to give some ideas of the techniques used in the proofs.
