Differential operators on an affine curve: ideal classes and Picard groups

Abstract

Let X be a smooth complex affine curve, and let R be the space of right ideal classes in the ring D of differential operators on X. We introduce and study a fibration γ: R \to Pic(X). We relate this fibration to the corresponding one in the classical limit, and derive an integer invariant $ n $ which indexes the decomposition of the fibres of γinto Calogero-Moser spaces (see [BC]). We also study the action of the group Pic(D) on our fibration; and we explain how to define γin the framework of the Grassmannian description of R due to Cannings and Holland.

12 pages