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

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 maximal and the minimal fixed component are both two dimensional, then $(M,{\omega }_M)$ is $S^1$-equivariantly symplectomorphic to some Kähler Fano manifold $(X,{\omega }_X,J)$ equipped with a certain holomorphic Hamiltonian $S^1$-action. We also give a complete list of all such Fano manifolds together with an explicit description of the corresponding $S^1$-actions.

arXiv comment40 pages, 17 figures. arXiv admin note: text overlap with arXiv:1812.09892