Let X be a smooth complex affine curve, and let R be the space of right ideal classes in the ring of differential operators on X. We introduce and study a fibration : R -> 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 into Calogero–Moser spaces. We also study the action of the group Pic on our fibration; and we explain how to define in the framework of the Grassmannian description of R due to Cannings and Holland.



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