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 $M$?