Smooth manifolds in $G_{n,2}$ and $\mathbb{C} P^{N}$ defined by symplectic reductions of $T^n$-action

We study symplectic reductions arising from the canonical action of the maximal compact torus $T^n$ on the complex Grassmann manifold $G_{n,2}$ as well as those arising from the $T^n$-action on the complex projective space $\C P^{N}$, $N=\binom{n}{2}-1$ for which the Plücker embedding $G_{n,2}\to \C