English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the Hamiltonian flow on complex complete intersection surfaceswith isolated singularities, equipped with the Jacobian Poisson structure. Moregenerally we consider complete intersections of arbitrary dimension equippedwith Hamiltonian flow with respect to the natural top polyvector field, whichone should view as a degenerate Calabi-Yau structure.  Our main result computes the coinvariants of functions under the Hamiltonianflow. In the surface case this is the zeroth Poisson homology, and our resultgeneralizes those of Greuel, Alev and Lambre, and the authors in thequasihomogeneous and formal cases. Its dimension is the sum of the dimension ofthe top cohomology and the sum of the Milnor numbers of the singularities. Inother words, this equals the dimension of the top cohomology of a smoothing ofthe variety.  More generally, we compute the derived coinvariants, which replaces the topcohomology by all of the cohomology. Still more generally we compute theD-module which represents all invariants under Hamiltonian flow, which is anontrivial 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 curvesof genus g, the extension on the top is the holomorphic half of the maximalextension.

Invariants of Hamiltonian flow on locally complete intersections