MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

One definition of Toric Kahler manifolds that I know is the following - $(M,J,\omega)$ is a Kahler manifold of dimension n with an $\textit{effective}$ $\textbf{T}^n$ action which preserves the symplectic form and the complex structure, where $\textbf{T}^n$ is the real torus of dimension n. Then

The action of $\textbf{T}^n$ extends to an action of $(\textbf{C}^*)^n$ on $(M,J,\omega)$. Is it automatically true that this action has a free, open, dense orbit sitting inside $M$?

share|cite|improve this question
This is true for any toric manifold (or toric variety): . In your definition you should add that $dim M=2n$. – Dmitri Jun 6 '11 at 20:52

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.