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arXiv · 1912.13172

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions

Yunhyung Cho
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Abstract

Let $(M,ω_M)$ be a six dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian $S^1$-action. We show that $(M,ω_M)$ is $S^1$-equivariant symplectomorphic to some Kähler Fano manifold $(X,ω_X, J)$ with a certain holomorphic $\mathbb{C}^*$-action. We also give a complete list of all such Fano manifolds and describe all semifree $\mathbb{C}^*$-actions on them specifically.

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Yunhyung Cho. 2019-12-31. Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions. https://arxiv.org/abs/1912.13172

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