The log-concavity conjecture on semifree symplectic S^1-manifolds with isolated fixed points

Yunhyung Cho

The log-concavity conjecture on semifree symplectic S^1-manifolds with isolated fixed points

Symplectic Geometry 2016-01-05 v2 Mathematical Physics math.MP

Authors: Yunhyung Cho

Abstract

Let $(M,\omega)$ be a closed $2n$ -dimensional semifree Hamiltonian $S^1$ -manifold with only isolated fixed points. We prove that a density function of the Duistermaat-Heckman measure is log-concave. Moreover, we prove that $(M,\omega)$ and any reduced symplectic form satisfy the Hard Lefschetz property.

Keywords

log-concavity Duistermaat-Heckman measure semifree Hamiltonian S^1-manifold isolated fixed points Hard Lefschetz property reduced symplectic form

Cite

@article{arxiv.1103.2998,
  title  = {The log-concavity conjecture on semifree symplectic S^1-manifolds with isolated fixed points},
  author = {Yunhyung Cho},
  journal= {arXiv preprint arXiv:1103.2998},
  year   = {2016}
}

Comments

12pages. 1 figure

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