A limit of toric symplectic forms that has no periodic Hamiltonians

Details A limit of toric symplectic forms that has no periodic Hamiltonians A limit of toric symplectic forms that has no periodic Hamiltonians

1998-10-19

arxiv.org/abs/math/9810122v1

Mathematics

Symplectic Geometry

7 pages, 2 external figures

Scientific paper

We calculate the Riemann-Roch number of some of the pentagon spaces defined in [Klyachko,Kapovich-Millson,HK1]. Using this, we show that while the regular pentagon space is diffeomorphic to a toric variety, even symplectomorphic to one under arbitrarily small perturbations of its symplectic structure, it does not admit a symplectic circle action. In particular, within the cohomology classes of symplectic structures, the subset admitting a circle action is not closed.

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