Resolution of Singularities of the Orbit Spaces $$G_{n,2}/T^n$$

We study the orbit space $$X_n = G_{n,2}/T^n$$ of standard action compact torus $$T^n$$ on complex Grassmann manifold $$G_{n,2}$$ . describe structure set critical points $$\operatorname{Crit}G_{n,2}$$ generalized moment map $$\mu_n \colon\, G_{n,2}\to \mathbb{R}^n$$ whose image is a hypersimplex $$\Delta_{n,2}$$ The canonical projection $$G_{n,2}\to X_n$$ maps $$\operatorname{Crit} G_{n,2}$$ to $$\operatorname{Crit}X_n$$ , which by definition consists orbits $$x\in with nontrivial stabilizer subgroup in $$T^{n-1}=T^n/S^1$$ where $$S^1\subset T^n$$ diagonal one-dimensional torus. Introducing notion singular point $$x\in\operatorname{Sing}X_n \subset terms parameter spaces orbits, we prove that $$Y_n X_n\setminus\operatorname{Sing}X_n$$ an open and dense $$X_n$$ show $$\operatorname{Crit}X_n \subset\operatorname{Sing}X_n$$ for $$n>4$$ but $$\operatorname{Sing}X_4\subset\operatorname{Crit}X_4$$ Our central result construction $$p_n U_n= \mathcal{F}_n\times\Delta_{n,2}\to $$\dim U_n \dim $$\mathcal{F}_n$$ universal space. Earlier, have proved closed smooth diffeomorphic known $$\,\overline{\!\mathcal{M}}(0,n)$$ Z_n p_n^{-1}(Y_n)\to Y_n$$ diffeomorphism, sets $$p_n^{-1}(x)$$ $$x\in\operatorname{Sing}X_n$$