Periodic Hamiltonian flows on four dimensional manifolds

1995/10/13 by Karshon, Yael · 4 citations
#53C55 (Secondary) #58F05 #70H33 (Primary) 53C12 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.dg-ga/9510004

Abstract

We classify the periodic Hamiltonian flows on compact four dimensional symplectic manifolds up to isomorphism of Hamiltonian S¹ spaces. Additionally, we show that all these spaces are Kaehler, that every such space is obtained from a simple model by a sequence of symplectic blowups, and that if the fixed points are isolated then the space is a toric variety.

Cited by

• Prime Fano 4-folds with semi-free torus actions
• On the equivariant cohomological rigidity of semi-free Hamiltonian circle actions
• C⁰-rigidity of the Hamiltonian diffeomorphism group of symplectic rational surfaces
• Hamiltonian torus actions and the unimodality of odd Betti numbers

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