Perverse bundles and Calogero-Moser spaces

We present a simple description of moduli spaces of torsion-free D-modules (D-bundles) on general smooth complex curves, generalizing the identification of the space of ideals in the Weyl algebra with CalogeroMoser quiver varieties. Namely, we show that the moduli of D-bundles form twisted cotangent bundles to moduli of torsion sheaves on X, answering a question of Ginzburg. The corresponding (untwisted) cotangent bundles are identified with moduli of perverse vector bundles on T^*X, which contain as open subsets the moduli of framed torsion-free sheaves (the Hilbert schemes T ^*X^[n] in the rank-one case). The proof is based on the description of the derived category of D-modules on X by a noncommutative version of the Beilinson transform on P¹.