Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions

Yunhyung Cho

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions

Symplectic Geometry 2020-01-01 v1 Algebraic Geometry

Authors: Yunhyung Cho

Abstract

Let $(M,\omega_M)$ be a six dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian $S^1$ -action. We show that $(M,\omega_M)$ 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.

Keywords

symplectic manifold circle action monotone kähler fano manifold equivariant symplectomorphism classification

Cite

@article{arxiv.1912.13172,
  title  = {Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions},
  author = {Yunhyung Cho},
  journal= {arXiv preprint arXiv:1912.13172},
  year   = {2020}
}

Comments

Complete version (with 110 pages and many figures). We have splitted this manuscript into three parts arXiv:1812.09892, arXiv:1904.10962, and arXiv:1905.07292

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions

Abstract

Keywords

Cite

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