Solitons: Differential equations, symmetries, and infinite-dimensional algebras
《Solitons: Differential equations, symmetries, and infinite-dimensional algebras》 · 第 213、215 页 · Section 8.4「The Grassmannian functor and its representability」与 Proposition 8.14
We define $\operatorname{Grass}_{d,n}(S)=\{\mathcal U\subseteq\mathcal O_S^n;\ \mathcal O_S^n/\mathcal U\text{ is a locally free }\mathcal O_S\text{-module of rank }n-d\}$. Then the functor $\operatorname{Grass}_{d,n}$ is representable. The representing scheme is called Grassmannian and is also denoted by $\operatorname{Grass}_{d,n}$.