# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1905.07292