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

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.

12pages. 1 figure

References in corpus (1)

• Semifree Hamiltonian circle actions on 6-dimensional symplectic manifolds with non-isolated fixed point set

Cited by in corpus (1)

• Log-concavity of complexity one Hamiltonian torus actions