The Varieties of Special Linear Series on a Curve

Abstract

As we have said, our approach to the study of curves is to analyze their projective realizations, and to speak of these is to speak of linear series. A more in-depth reflection leads to the appreciation of the fact that it is not only the single linear series which are important, but rather the configuration of all linear series of given type that a curve carries. To make precise what these “configurations” are we shall introduce three main kinds of varieties, which we now describe set-theoretically.