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

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

2011-03-15

arxiv.org/abs/1103.2998v2

Mathematics

Symplectic Geometry

12pages. 1 figure

Scientific paper

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.

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