for a given genus "g", the moduli space for curves "c" of genus "g" should contain a dense subset parameterizing those curves with the minimum in the way of special divisors. one goal of the theory is to 'count constants', for those curves: to predict the dimension of the space of special divisors (up to linear equivalence) of a given degree "d", as a function of "g", that "must" be present on a curve of that genus.