Cеминары "Комбинаторика инвариантов": Матвей Сергеев

M.Kapranov has shown that the moduli space $\overline{\mathcal{M}}_{0,n}$ of stable genus 0 curves with $n$ marked points coincides with the Chow factor of the Grassmannian $G_{n,2}$ modulo the standard torus $(C^*)^n$ action. As recent papers by V.Buchstaber and S.Terzic show, the Chow factor in question is closely related to the space of orbits $G_{n,2}/T^{n}$  of the standard torus $T^n = (S^1)^n$ action on $G_{n,2}$. Moreover, the space of orbits $G_{n,2}/T^{n}$  can be considered as the universal (initial) object of the Hasset category the objects in which are moduli spaces  $\overline{\mathcal{M}}_{0,\mathcal{A}}$ of weighted stable genus 0 curves. The complexity of the action of $T^n$ on $G_{n,2}$ is positive, whence the moment polytope, which  is the hypersymplex $\Delta_{n,2}$, does not allow one to describe the space of orbits $G_{n,2}/T^n$ completely. In this case, Buchstaber and Terzic reduced the problem to constructing a chamber decomposition of the hypersymplex $\Delta_{n,2}$. A new chamber decomposition in terms of graphs obtained recently by the speaker will be described in the talk.