  In these notes, we give a survey of the main results of [BC] and [BW]. Our
aim is to generalize the geometric classification of (one-sided) ideals of the
first Weyl algebra $ A_1(C) $ (see [BW1, BW2]) to the ring $ D(X) $ of
differential operators on an arbitrary complex smooth affine curve X. We
approach this problem in two steps: first, we classify the ideals of D(X) up to
stable isomorphism, in terms of the Picard group of X; then, we refine this
classification by describing each stable isomorphism class as a disjoint union
of (certain quotients of) generalized Calogero-Moser spaces C_n(X, I). The
latter are defined as representation varieties of deformed preprojective
algebras over a one-point extension of the ring of regular functions on X by
the line bundle I. As in the classical case, C_n(X, I) turn out to be smooth
irreducible varieties of dimension 2n.
