  Let X be a complex smooth affine irreducible curve, and let D = D(X) be the
ring of global differential operators on X. In this paper, we give a geometric
classification of left ideals in $ D $ and study the natural action of the
Picard group of D on the space J(D) of isomorphism classes of such ideals. We
recall that, up to isomorphism in the Grothendieck group K_0(D), the ideals of
D are classified by the Picard group of X: there is a natural fibration \gamma:
J(D) \to Pic(X), whose fibres are the stable isomorphism classes of ideals of D
(see \cite{BW}). In this paper, we refine this classification by describing the
fibres of \gamma in terms of finite-dimensional algebraic varieties C_n(X, I),
which we call the (generalized) Calogero-Moser spaces. We define these
varieties as representation varieties of deformed preprojective algebras over a
certain extension of the ring of regular functions on $ X $. As in the
classical case (see \cite{Wi}), we prove that C_n(X, I) are smooth affine
irreducible varieties of dimension 2n. Our results generalize the description
of left ideals of the first Weyl algebra A_1(C) in \cite{BW1, BW2}; however,
our methods are quite different.
