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

TL;DR

This paper completes the classification of six-dimensional closed monotone symplectic manifolds with semifree Hamiltonian circle actions, showing they are equivalent to certain Kähler Fano manifolds with holomorphic circle actions.

Contribution

It finalizes the classification of these manifolds and establishes their symplectomorphic equivalence to specific Kähler Fano manifolds.

Findings

Complete classification of six-dimensional monotone symplectic manifolds with semifree circle actions.

Every such manifold is symplectomorphic to a Kähler Fano manifold with a holomorphic circle action.

Abstract

In this paper, we complete the classification of six-dimensional closed monotone symplectic manifolds admitting semifree Hamiltonian $S^1$-actions. We also show that every such manifold is $S^1$-equivariantly symplectomorphic to some K\"{a}ahler Fano manifold with a certain holomorphic Hamiltonian circle action.