A limit of toric symplectic forms that has no periodic Hamiltonians
Abstract
We calculate the RiemannRoch number of some of the pentagon spaces defined in [Klyachko,KapovichMillson,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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 1998
 DOI:
 10.48550/arXiv.math/9810122
 arXiv:
 arXiv:math/9810122
 Bibcode:
 1998math.....10122H
 Keywords:

 Symplectic Geometry
 EPrint:
 7 pages, 2 external figures