Seminar

I compute the coinvariants of functions under Hamiltonian flow for complete intersections with isolated singularities. For surfaces the Hamiltonian flow is with respect to the Jacobian Poisson structure; in higher dimensions the Hamiltonian flow can be generalized using the natural top polyvector field which can be thought of as a degenerate Calabi-Yau structure. In particular the dimension of the coinvariant space equals the sum of the dimension of the top cohomology of the singular variety with the sum of the Milnor numbers of the singularities. In other words this equals the top cohomology of the smoothing of the variety. These results follow from more general ones computing the D-module which represents invariants under the Hamiltonian flow. The structure is interesting: it turns out to have a summand which is the maximal extension on the bottom, but not on the top, of the intersection cohomology D-module. This is joint work with Pavel Etingof.