A limit of toric symplectic forms that has no periodic Hamiltonians
Symplectic Geometry
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/9810122,
title = {A limit of toric symplectic forms that has no periodic Hamiltonians},
author = {Jean-Claude Hausmann and Allen Knutson},
journal= {arXiv preprint arXiv:math/9810122},
year = {2007}
}
Comments
7 pages, 2 external figures