List questions from zariski-topology

Published on 14 Sep 2023 - 7:05

30

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$Spec(R)$ finite and discrete implies $R_{red}$ Artinian proof verification

Published on 25 Mar 2026 - 14:05

59

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Need help in competing the proof of $V_K(I_K (E)) = \overline{E}$

Published on 23 Sep 2023 - 11:48

55

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Zariski Topology on $\mathbb{A}^1$

Published on 04 Oct 2023 - 19:03

103

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Proof that the image of $(x,y) \mapsto (x, xy)$ is neither open, closed nor locally closed.

Published on 12 Oct 2023 - 19:53

89

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how to prove that a set is not algebraic

Published on 29 Oct 2023 - 13:08

316

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The complement of an algebraic set in $\mathbb{P}^n$ is path-connected

Published on 31 Oct 2023 - 7:45

83

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Zariski topology on $\mathbb{P^n}$

Published on 07 Nov 2023 - 8:58

68

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All the open affine subsets of $\mathbb{A}^1 \subseteq \mathbb{P}^1$. Are open affine subsets always Zariski open?

Published on 15 Nov 2023 - 16:44

45

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Is open always Zariski open in the context of Algebraic geometry, unless otherwise mentioned?

Published on 16 Nov 2023 - 8:18

96

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Image of a projective variety is a projective variety

Published on 17 Nov 2023 - 10:47

37

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On the finiteness of certain Zariski closed subsets of the prime spectrum of commutative Noetherian local rings

Published on 25 Mar 2026 - 21:51

184

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Question about exc. $15.2.21.$b in Dummit and Foote.

Published on 03 Jan 2024 - 2:52

55

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Prove $S = \{ (a,b) \in \mathbb{A}^2 \ | \ a \overline{a} + b \overline{b} = 1\}$ is not Zariski closed

Published on 20 Jan 2024 - 8:07

58

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Hausdorff-ness of irreducible affine algebraic sets

Published on 24 Jan 2024 - 23:18

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Subbasis of Zariski topology on $\mathbb R^n$.

$Spec(R)$ finite and discrete implies $R_{red}$ Artinian proof verification

Need help in competing the proof of $V_K(I_K (E)) = \overline{E}$

Zariski Topology on $\mathbb{A}^1$

Proof that the image of $(x,y) \mapsto (x, xy)$ is neither open, closed nor locally closed.

how to prove that a set is not algebraic

The complement of an algebraic set in $\mathbb{P}^n$ is path-connected

Zariski topology on $\mathbb{P^n}$

All the open affine subsets of $\mathbb{A}^1 \subseteq \mathbb{P}^1$. Are open affine subsets always Zariski open?

Is open always Zariski open in the context of Algebraic geometry, unless otherwise mentioned?

Image of a projective variety is a projective variety

On the finiteness of certain Zariski closed subsets of the prime spectrum of commutative Noetherian local rings

Question about exc. $15.2.21.$b in Dummit and Foote.

Prove $S = \{ (a,b) \in \mathbb{A}^2 \ | \ a \overline{a} + b \overline{b} = 1\}$ is not Zariski closed

Hausdorff-ness of irreducible affine algebraic sets

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