List questions from projective-space

Published on 20 Nov 2020 - 15:58

309

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Using Cellular Cohomology for computing $H^n(\mathbb{RP}^n,\mathbb{RP}^{n-1})$, Hatcher's Theorem 3.19.

Published on 20 Nov 2020 - 18:39

73

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If $f: X \rightarrow \mathbb{P}^n$ is a regular map and $U \subset X$ is constructible, then $f(U)$ is constructible.

Published on 21 Nov 2020 - 1:45

340

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Emedding of $\mathbb{ RP}^3$

Published on 29 Mar 2026 - 11:08

98

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Presentation of projective variety example

Published on 27 Mar 2026 - 4:22

109

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Homeomorphism between $\mathbb{P}^n$ and $D^n / R$

Published on 26 Nov 2020 - 16:03

172

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Vanishing of a non-constant function on projective variety

Published on 26 Mar 2026 - 8:04

391

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How to show that $P(\mathbb R^n$) admits a positive sectional curvature?

Published on 30 Nov 2020 - 4:57

92

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How to understand the spin structures on $T^d$ and $\mathbb{RP}^d$

Published on 27 Mar 2026 - 7:13

270

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Show that the inclusion $\mathbb{RP}^2\to\mathbb{RP}^3$ induced by the inclusion $S^2\to S^3$ is not homotopic to the constant map

Published on 02 Dec 2020 - 22:55

151

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Special Case for Bézout Theorem

Published on 04 Dec 2020 - 20:09

61

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Attaching disks and contracting is equivalent to taking quotients.

Published on 25 Mar 2026 - 20:41

311

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Construction of $\mathbb{CP}^2$ from $S^2\times S^2$

Published on 08 Dec 2020 - 13:52

49

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$\mathbb{CP}^{2}$ is homeomorphic to $ ( S^2 \times S^2)/\mathbb{Z}_2$

Published on 08 Dec 2020 - 14:38

585

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Part (a) of Exercise 5.14 in Chapter II of Hartshorne: Show that $\bigoplus_{n\geq 0}\Gamma(X,\mathcal{O}_X(n))$ is the integral closure of $S$.

Published on 09 Dec 2020 - 8:30

List Question

Notion of cusp in algebraic geometry

Using Cellular Cohomology for computing $H^n(\mathbb{RP}^n,\mathbb{RP}^{n-1})$, Hatcher's Theorem 3.19.

If $f: X \rightarrow \mathbb{P}^n$ is a regular map and $U \subset X$ is constructible, then $f(U)$ is constructible.

Emedding of $\mathbb{ RP}^3$

Presentation of projective variety example

Homeomorphism between $\mathbb{P}^n$ and $D^n / R$

Vanishing of a non-constant function on projective variety

How to show that $P(\mathbb R^n$) admits a positive sectional curvature?

How to understand the spin structures on $T^d$ and $\mathbb{RP}^d$

Show that the inclusion $\mathbb{RP}^2\to\mathbb{RP}^3$ induced by the inclusion $S^2\to S^3$ is not homotopic to the constant map

Special Case for Bézout Theorem

Attaching disks and contracting is equivalent to taking quotients.

Construction of $\mathbb{CP}^2$ from $S^2\times S^2$

$\mathbb{CP}^{2}$ is homeomorphic to $ ( S^2 \times S^2)/\mathbb{Z}_2$

Part (a) of Exercise 5.14 in Chapter II of Hartshorne: Show that $\bigoplus_{n\geq 0}\Gamma(X,\mathcal{O}_X(n))$ is the integral closure of $S$.

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