English

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