The orbit spaces $G_{n,2}/T^n$ and the Chow quotients $G_{n,2}//(\mathbb C^{\ast})^n$ of the Grassmann manifolds $G_{n,2}$

The complex Grassmann manifolds Gn,k appear as one of the fundamental objects in developing an interaction between algebraic geometry and algebraic topology. The case k=2 is of special interest on its own as the manifolds Gn,2 have several remarkable properties which distinguish them from the Gn,k for k>2.
In our paper we obtain results which, essentially using the specifics of the Grassmann manifolds Gn,2, develop connections between algebraic geometry and equivariant topology. They are related to well-known problems of the canonical action of the algebraic torus (C∗)n on Gn,2 and the induced action of the compact torus Tn⊂(C∗)n.
Kapranov proved that the Deligne-Mumford-Grothendieck-Knudsen compactification ¯M(0,n) of the space of n-pointed rational stable curves can be realized as the Chow quotient Gn,2//(C∗)n. In recent papers of the authors a constructive description of the orbit space Gn,2/Tn was obtained. In deducing this result the notions of the complex of admissible polytopes and the universal space of parameters Fn for the Tn-action on Gn,2 were of essential use.
Using the techniques of wonderful compactification, in this paper an explicit construction of the space Fn is presented. In combination with Keel's description of ¯M(0,n), this construction enabled one to obtain an explicit diffeomorphism between Fn and ¯M(0,n). In this way, we give a description of Gn,2//(C∗)n as the space Fn with a structure described in terms of admissible polytopes Pσ and spaces Fσ.