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

2018/12/24 by Cho, Yunhyung · 2 citations
#14J45 #53D20 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1812.09892

Abstract

Let (M,ω_M) be a six dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian S¹-action. We show that if the minimal (or maximal) fixed component of the action is an isolated point, then (M,ω_M) is S¹-equivariant symplectomorphic to some Kähler Fano manifold (X,ω_X, J) with a certain holomorphic ℂ^*-action. We also give a complete list of all such Fano manifolds and describe all semifree ℂ^*-actions on them specifically.

Cited by

• Prime Fano 4-folds with semi-free torus actions
• On the equivariant cohomological rigidity of semi-free Hamiltonian circle actions

Related

• Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions
• Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions II
• Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions III
• Semi-free Hamiltonian circle actions on 6 dimensional symplectic manifolds
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