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arXiv · 1103.2998

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

Yunhyung Cho
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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.

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Yunhyung Cho. 2011-03-15. The log-concavity conjecture on semifree symplectic S^1-manifolds with isolated fixed points. https://arxiv.org/abs/1103.2998

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