  We consider the Hamiltonian flow on complex complete intersection surfaces
with isolated singularities, equipped with the Jacobian Poisson structure. More
generally we consider complete intersections of arbitrary dimension equipped
with Hamiltonian flow with respect to the natural top polyvector field, which
one should view as a degenerate Calabi-Yau structure.
  Our main result computes the coinvariants of functions under the Hamiltonian
flow. In the surface case this is the zeroth Poisson homology, and our result
generalizes those of Greuel, Alev and Lambre, and the authors in the
quasihomogeneous and formal cases. Its dimension is the sum of the dimension of
the top cohomology and the sum of the Milnor numbers of the singularities. In
other words, this equals the dimension of the top cohomology of a smoothing of
the variety.
  More generally, we compute the derived coinvariants, which replaces the top
cohomology by all of the cohomology. Still more generally we compute the
D-module which represents all invariants under Hamiltonian flow, which is a
nontrivial extension (on both sides) of the intersection cohomology D-module,
which is maximal on the bottom but not on the top. For cones over smooth curves
of genus g, the extension on the top is the holomorphic half of the maximal
extension.
