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

Abstract

This is the second of the series of papers on the classification of six-dimensional closed monotone symplectic manifold admitting a semifree Hamiltonian [Formula: see text]-action. In [Y. Cho, Classification of six-dimensional monotone symplectic manifolds admitting semifree circle actions I, Int. J. Math. 6 1950032], we dealt with the case where at least one of the extremal fixed point is isolated and proved that every such manifold is Kähler Fano. In this paper, we show that if the maximal and the minimal fixed components are both two-dimensional, then the manifold is [Formula: see text]-equivariantly symplectomorphic to some Kähler Fano manifold with a certain holomorphic Hamiltonian [Formula: see text]-action. We also give a complete list of such Fano manifolds together with an explicit description of the [Formula: see text]-actions.