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

Abstract

Let [Formula: see text] be a six-dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian [Formula: see text]-action. We show that if the minimal (or maximal) fixed component of the action is an isolated point, then [Formula: see text] is [Formula: see text]-equivariantly symplectomorphic to some Kähler Fano manifold [Formula: see text] with a certain holomorphic [Formula: see text]-action. We also give a complete list of all such Fano manifolds and describe all semifree [Formula: see text]-actions on them specifically.