Let X be a smooth affine algebraic curve over C with coordinate ring O(X), andlet D(X) denote the ring of (global) algebraic differential operators on X. Recall that a holomorphic function f on X is called holonomic if its annihilator ideal Ann(f) ⊆ D(X) is non-zero. It is known that the left ideals in D(X) are classified geometrically in two ways: 1. In terms of the adelic Grassmannian Gr^{ad}, that parametrises certain infinite- dimensional subspaces of O(X), up to equivalence. 2. In terms of certain finite-dimensional algebraic varieties C_n(X), called Calogero-Moser spaces. In this thesis, we study the invariants of a holomorphic function f on X that arise geometrically from Ann(f). In particular, we give a direct construction that assigns to a given left ideal M ⊆ D(X) a finite dimensional space of conditions dual to the point in Gr^{ad} corresponding to M. Using this dual description, we give an explicit formula for the Calogero-Moser invariant n(M) - the index of the Calogero-Moser Stratum C_n(X) that M lies in. The main results of this thesis are part of a joint work with Yuri Berest that will appear in [BG].