In this section
@article{Schedler:2016:10.1007/s00029-016-0232-3,
author = {Schedler, TJ and Proudfoot, NJ},
doi = {10.1007/s00029-016-0232-3},
journal = {Selecta Mathematica},
pages = {179--202},
title = {Poisson–de Rham homology of hypertoric varieties and nilpotent cones},
url = {http://dx.doi.org/10.1007/s00029-016-0232-3},
volume = {23},
year = {2016}
}
TY - JOUR
AB - We prove a conjecture of Etingof and the second author for hypertoric varieties that the Poisson–de Rham homology of a unimodular hypertoric cone is isomorphic to the de Rham cohomology of its hypertoric resolution. More generally, we prove that this conjecture holds for an arbitrary conical variety admitting a symplectic resolution if and only if it holds in degree zero for all normal slices to symplectic leaves. The Poisson–de Rham homology of a Poisson cone inherits a second grading. In the hypertoric case, we compute the resulting 2-variable Poisson–de Rham–Poincaré polynomial and prove that it is equal to a specialization of an enrichment of the Tutte polynomial of a matroid that was introduced by Denham (J Algebra 242(1):160–175, 2001). We also compute this polynomial for S3-varieties of type A in terms of Kostka polynomials, modulo a previous conjecture of the first author, and we give a conjectural answer for nilpotent cones in arbitrary type, which we prove in rank less than or equal to 2.
AU - Schedler,TJ
AU - Proudfoot,NJ
DO - 10.1007/s00029-016-0232-3
EP - 202
PY - 2016///
SN - 1022-1824
SP - 179
TI - Poisson–de Rham homology of hypertoric varieties and nilpotent cones
T2 - Selecta Mathematica
UR - http://dx.doi.org/10.1007/s00029-016-0232-3
UR - http://hdl.handle.net/10044/1/31129
VL - 23
ER -