Invariants of Hamiltonian flow on locally complete intersections
Name
Etingof_Invariants of.pdf
Size
299.67 KB
Format
Adobe PDF
Checksum (MD5)
a0a0868dfd2955e807526f5b239cdff5
Author(s)
Schedler, Travis
Etingof, Pavel I.
Date Issued
September 2014
Journal
Geometric and Functional Analysis
Publisher
Springer-Verlag
Citation
Etingof, Pavel, and Travis Schedler. “Invariants of Hamiltonian Flow on Locally Complete Intersections.” Geometric and Functional Analysis 24, no. 6 (September 23, 2014): 1885–1912.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00039-014-0302-7
