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.