# Tagged Questions

42 views

### Affine stratification of Grassmannian $\mathbb{G}(1,\mathbb{P}^3)$

Let $G=\mathbb{G}(1,\mathbb{P})$ be the Grassmannian variety of lines in $\mathbb{P}^3$. I have to do an affine stratification of $G$. In order to do this we consider the flag $\mathcal{F}$ of the ...
193 views

### fixed point projective geometry

I am thinking about the following: Let $\sigma:\mathbb C P^n\rightarrow\mathbb C P^n$ be a projectivity with $\sigma\circ\sigma=id_{\mathbb C P^n}$. I define the set of all fix points by ...
100 views

The way I define the cross-ratio in projectve geometry: Let $P_0,P_1,P_2,P_3$ being four points on a projective line G, such that $P_0,P_1,P_2$ are pairwise distinct. Let $\pi:\mathbb KP^1\rightarrow ... 1answer 107 views ### Cross-ratio projective geometry I have 4 points$P_0=[1:2], P_1=[3:4], P_2=[5:6], P_3=[7,8]$in$\mathbb KP^1$and would like to evaluate the cross-ratio. It is given by the following:$\pi:\mathbb KP^1\rightarrow G$is the unique ... 1answer 108 views ### Lines projective space I have a question concerning the answer of Georges Elencwajg in Lines in projective space There he states that the line$\overline {AB}=\mathbb P(\Lambda)\subset \mathbb P^n$has its points of the ... 1answer 90 views ### Projective geometry well defined bijection I consider the sphere$\mathbb S^n:=\{x\in\mathbb R^{n+1}: \|x\|=1 \}$and the equivalence relation$x\sim y:\Leftrightarrow x=\pm y$. How can it be shown that the inclusion$\mathbb ...
For $j=0,\ldots,n$ consider the affine hyperplane $A_j:=e_j+\langle e_0,\ldots,e_{j-1},e_{j+1},\ldots,e_n\rangle$ in $\mathbb K^{n+1}$ and the associated embedding \$\tau_j:\mathbb ...