The log-concavity conjecture for the Duistermaat-Heckman measure revisited
| dc.creator | Lin, Yi | |
| dc.date | 2007-03-10 | |
| dc.date | 2008-03-03 | |
| dc.date.accessioned | 2026-07-07T09:24:07Z | |
| dc.date.available | 2026-07-07T09:24:07Z | |
| dc.description | Karshon constructed the first counterexample to the log-concavity conjecture for the Duistermaat-Heckman measure: a Hamiltonian six manifold whose fixed points set is the disjoint union of two copies of $T^4$. In this article, for any closed symplectic four manifold $N$ with $b+$ greater than 1, we show that there is a Hamiltonian six manifold $M$ such that its fixed points set is the disjoint union of two copies of $N$ and such that its Duistermaat-Heckman function is not log-concave. On the other hand, we prove that if there is a torus action of complexity two such that all the symplectic reduced spaces taken at regular values satisfy the condition $b+=1$, then its Duistermaat-Heckman function has to be log-concave. As a consequence, we prove the log-concavity conjecture for Hamiltonian circle actions on six manifolds such that the fixed points sets have no four dimensional components, or only have four dimensional pieces with $b+=1$. | |
| dc.description | This is the version which is going to appear in Inter. Math. Research Notices. A few references are added. Some minor mistakes are corrected | |
| dc.identifier | https://arxiv.org/abs/math/0703297 | |
| dc.identifier | http://arxiv.org/abs/math/0703297 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155983 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | 53D20 | |
| dc.title | The log-concavity conjecture for the Duistermaat-Heckman measure revisited | |
| dc.type | text |