Universal spaces of parameters for complex Grassmann manifolds $G_{q+1,2}$

TL;DR

This paper constructs a universal parameter space for complex Grassmann manifolds $G_{q+1,2}$, extending previous work on $G_{5,2}$, using moduli spaces of genus zero stable curves.

Contribution

It introduces a new universal space of parameters for $G_{q+1,2}$, generalizing prior constructions and utilizing moduli space techniques.

Findings

Constructed universal space for $G_{q+1,2}$.

Extended the framework from $G_{5,2}$ to general $q$.

Connected Grassmannian parameters with moduli space of stable curves.

Abstract

Buchstaber and Terzic introduced a notion of universal space of parameters $\mathcal{F}$ for a manifold $M^{2n}$, which has an effective action of compact torus $T^k$ , $k \leq n$ with some additional properties. with special properties. This space is needed to construction of factor $M^{2n}/T^k$. Buchstaber and Terzic constructed the universal space of parameters for $G_{5,2}$. In this work we construct universal space of parameters for complex Grassmann manifold $G_{q+1,2}$. Our construction is based on the construction of moduli space of stable curves of genus zero with $q+1$ marked points due to Salamon, McDuff and Hofer.