Toric Topology of the complex Grassmann manifolds G(n,2)

Abstract: In toric topology and toric geometry, a model example is the complex projective space $\mathbb{CP}^n$ equipped with the standard actions of $T^{n+1} = (U(1))^{n+1}$ and $(\mathbb{C}^*)^{n+1}$, respectively. In this case, the complexity of the actions is zero, and hence the orbit space $\mathbb{CP}^n/T^{n+1}$ is homeomorphic to the moment polytope — the simplex $\Delta^n$. Recently, V. M. Buchstaber and S. Terzi\'c introduced a new theory for torus actions of positive complexity. A model example for these actions is the manifold of lines in $\mathbb{CP}^{n-1}$, i.e., the complex Grassmann manifold $G(n,2)$ equipped with the standard $T^n$ action. The moment polytope — the hypersimplex $\Delta(n,2)$ — is not sufficient to describe the orbit space $G(n,2)/T^n$. Buchstaber and Terzić constructed a topological model for this orbit space. A key ingredient is the universal space of parameters $\mathcal{F}$, which is a smooth compact manifold, and a projection $\pi \colon \Delta(n,2)\times \mathcal{F} \to G(n,2)/T^n$. The universal space of parameters is isomorphic to the Chow quotient $G(n,2)//(\mathbb{C}^*)^n$, introduced by I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky. In this talk, we will discuss the construction of the Buchstaber–Terzi\'c model.

mathematical physicsalgebraic geometryalgebraic topologygeometric topologyquantum algebra

Audience: researchers in the topic

Moscow-Beijing topology seminar

Series comments: https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1h.. Meeting ID: 818 6674 5751 Passcode: 141592