With T. Nevins.  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 X, generalizing the identification of the space of ideals in the Weyl algebra with Calogero-Moser quiver varieties. Namely we show that the moduli of D-bundles form twisted cotangent bundles to stacks 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 the projective line.