|
8
4
|
I have in mind the following question for some time. Is there an example of a compact symplectic manifold with a Hamiltonian S^1 action with isolated fixed points, that does not admit a compatible S^1 invariant Kahler strucutre? One would say, of course there should be such an example. But I have not seen any... Added. Apperently this is an open problem. |
|||
|
|
4
|
Lerman has constructed such an example see http://arxiv.org/abs/dg-ga/9601012v1 , well it has an isolated fixed point but also some fixed connected submanifolds, so maybe not exactly what you want. The construction has been later revisited by Kim http://www.mathjournals.org/mrl/2002-009-004/2002-009-004-002.pdf (note to editors: I guess the creation of 'torus-action' tag migh be useful.) |
||||||||||||
|
|
1
|
Sue Tolman has shown that there are non-Kahler 6-dimensional manifolds admitting Hamiltonian 2-torus actions all of whose fixed points are isolated ( http://arxiv.org/abs/dg-ga/9511007 ) . This might be a good first place to look to see if one of the components of the action satisfy the criteria you want. Interestingly, Karshon has shown ( in dg-ga/9510004 [sorry, I can only post one link as a new user]) that if a 4-manifold admits a Hamiltonian circle action, it must be Kahler. |
||||||
|
