Question

Show that there exists a coordinate system in $\mathbb{P}^n$ such that $P_0=(1:0:\cdots:0),\ldots,P_n=(0:0:\cdots:1),P_{n+1}=(1:\cdots:1)$

score 62 · Answer 1 · 2015-06-21 00:13:48

62

Views

Show that there exists a coordinate system in $\mathbb{P}^n$ such that $P_0=(1:0:\cdots:0),\ldots,P_n=(0:0:\cdots:1),P_{n+1}=(1:\cdots:1)$

Published on 21 Jun 2015 - 0:13

score 2.8k · Answer 2 · 2026-03-25 15:41:17

2.8k

Views

Show that any quadric in $\mathbb{P}^3$ is isomorphic to $\mathbb{P}^1 \times \mathbb{P}^1$

Published on 25 Mar 2026 - 15:41

score 97 · Answer 3 · 2015-06-25 21:44:01

97

Views

Given a point $P$ and a hyperplane $H$ in $\mathbb{P}^n$ such that $P \in H$, there is $T$ linear such that $T(P)=(0:\cdots:0:1)$ and $H:X_0=0$

Published on 25 Jun 2015 - 21:44

score 8.4k · Answer 4 · 2015-06-27 03:11:37

8.4k

Views

Real Projective Space Homeomorphism to Quotient of Sphere (Proof)

Published on 27 Jun 2015 - 3:11

score 295 · Answer 5 · 2026-03-28 10:16:43

295

Views

The projective space of all lines through the origin

Published on 28 Mar 2026 - 10:16

score 1.4k · Answer 6 · 2015-07-03 15:45:52

1.4k

Views

Complex Projective Space as a Quotient of a Disc

Published on 03 Jul 2015 - 15:45

score 162 · Answer 7 · 2015-07-06 07:40:54

162

Views

Homotopy type of intersection of complement of hyperplanes in projective space.

Published on 06 Jul 2015 - 7:40

score 421 · Answer 8 · 2015-07-11 02:21:57

421

Views

actions of $\mathbb{Z}_2$ on spheres

Published on 11 Jul 2015 - 2:21

score 1k · Answer 9 · 2026-03-28 10:17:22

1k

Views

Affine varieties over finite fields

Published on 28 Mar 2026 - 10:17

score 153 · Answer 10 · 2015-07-21 22:44:08

153

Views

Intuitive argument for the transitivity of $PGL(n+1)$ acting on $\mathbb{P}^n$

Published on 21 Jul 2015 - 22:44

score 448 · Answer 11 · 2026-03-25 11:11:56

448

Views

K-theory of projective space

Published on 25 Mar 2026 - 11:11

score 82 · Answer 12 · 2015-07-30 20:16:17

82

Views

How would one define polynomials over the projective line $P_K^1$

Published on 30 Jul 2015 - 20:16

score 6.9k · Answer 13 · 2026-03-30 06:47:26

6.9k

Views

Real Projective Plane is Same as Identifying Antipodal Boundary Points of The $2$-Disc.

Published on 30 Mar 2026 - 6:47

score 378 · Answer 14 · 2015-08-13 08:37:57

378

Views

Alternative definition of projective space

Published on 13 Aug 2015 - 8:37

score 380 · Answer 15 · 2026-03-25 12:44:15

380

Views

Does the exceptional Lie algebra $\mathfrak{g}_2$ arise from the isometry group of any projective space?

Published on 25 Mar 2026 - 12:44

List Question

Show that there exists a coordinate system in $\mathbb{P}^n$ such that $P_0=(1:0:\cdots:0),\ldots,P_n=(0:0:\cdots:1),P_{n+1}=(1:\cdots:1)$

Show that any quadric in $\mathbb{P}^3$ is isomorphic to $\mathbb{P}^1 \times \mathbb{P}^1$

Given a point $P$ and a hyperplane $H$ in $\mathbb{P}^n$ such that $P \in H$, there is $T$ linear such that $T(P)=(0:\cdots:0:1)$ and $H:X_0=0$

Real Projective Space Homeomorphism to Quotient of Sphere (Proof)

The projective space of all lines through the origin

Complex Projective Space as a Quotient of a Disc

Homotopy type of intersection of complement of hyperplanes in projective space.

actions of $\mathbb{Z}_2$ on spheres

Affine varieties over finite fields

Intuitive argument for the transitivity of $PGL(n+1)$ acting on $\mathbb{P}^n$

K-theory of projective space

How would one define polynomials over the projective line $P_K^1$

Real Projective Plane is Same as Identifying Antipodal Boundary Points of The $2$-Disc.

Alternative definition of projective space

Does the exceptional Lie algebra $\mathfrak{g}_2$ arise from the isometry group of any projective space?

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