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arXiv · 1812.09892

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions I

Yunhyung Cho
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Abstract

Let $(M,\omega_M)$ be a six dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian $S^1$-action. We show that if the minimal (or maximal) fixed component of the action is an isolated point, then $(M,\omega_M)$ is $S^1$-equivariant symplectomorphic to some K\"{a}hler Fano manifold $(X,\omega_X, J)$ 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. 2018-12-24. Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions I. https://arxiv.org/abs/1812.09892

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