  We relate Nakajima Quiver Varieties (or, rather, their multiplicative
version) with moduli spaces of perverse sheaves. More precisely, we consider a
generalization of the concept of perverse sheaves: microlocal sheaves on a
nodal curve X. They are defined as perverse sheaves on normalization of X with
a Fourier transform condition near each node and form an abelian category M(X).
One has a similar triangulated category DM(X) of microlocal complexes. For a
compact X we show that DM(X) is Calabi-Yau of dimension 2. In the case when all
components of X are rational, M(X) is equivalent to the category of
representations of the multiplicative pre-projective algebra associated to the
intersection graph of X. Quiver varieties in the proper sense are obtained as
moduli spaces of microlocal sheaves with a framing of vanishing cycles at
singular points. The case when components of X have higher genus, leads to
interesting generalizations of preprojective algebras and quiver varieties. We
analyze them from the point of view of pseudo-Hamiltonian reduction and
group-valued moment maps.
