List questions from affine-varieties

Published on 11 Apr 2026 - 20:49

228

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Does isomorphism of affine varieties preserve closed sets and open sets?

Published on 17 Apr 2026 - 1:20

47

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Why is $ \mathbb{K}[X] \otimes_{\mathbb{K}} \mathbb{K}[Y] \longrightarrow \mathbb{K}[X \times Y] $ surjective?

Published on 15 Apr 2026 - 16:52

76

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Kernel of a morphism of affine varieties is closed?

Published on 13 Apr 2026 - 10:48

542

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fiber product of affine varieties is associative?

Published on 10 Apr 2026 - 0:48

120

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Is fiber product of two affine varieties the same as Cartesian product as sets?

Published on 11 Apr 2026 - 0:22

46

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Characterization: Automorphisms of $\mathbb{A}_{\mathbb{C}}^n$

Published on 14 Apr 2026 - 4:03

371

Views

How does an affine algebraic group become a group scheme?

Published on 08 Apr 2026 - 16:46

69

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What is needed to arrive at Bézout's theorem in Algebraic Geometry?

Published on 16 Apr 2026 - 17:39

125

Views

Questions related to the definition of action of algebraic group $G$ that is locally algebraic

Published on 11 Apr 2026 - 1:14

66

Views

Does $k[X]$ always have a countable basis? ($X$ is an affine variety)

Published on 16 Apr 2026 - 3:09

195

Views

Question about motivation for upgrading varieties to schemes (nilpotency)

Published on 09 Apr 2026 - 10:51

126

Views

Projective variety $V_p(x^2 y - z^3)$ is singular

Published on 14 Apr 2026 - 16:10

662

Views

Definition of the Fibre of a Sheaf

Published on 14 Apr 2026 - 7:04

702

Views

Upper Semi-Continuity of the Rank of the Fibre of a Sheaf

Published on 15 Apr 2026 - 20:26

List Question

Simple question about affine varieties and coordinate rings

Does isomorphism of affine varieties preserve closed sets and open sets?

Why is $ \mathbb{K}[X] \otimes_{\mathbb{K}} \mathbb{K}[Y] \longrightarrow \mathbb{K}[X \times Y] $ surjective?

Kernel of a morphism of affine varieties is closed?

fiber product of affine varieties is associative?

Is fiber product of two affine varieties the same as Cartesian product as sets?

Characterization: Automorphisms of $\mathbb{A}_{\mathbb{C}}^n$

How does an affine algebraic group become a group scheme?

What is needed to arrive at Bézout's theorem in Algebraic Geometry?

Questions related to the definition of action of algebraic group $G$ that is locally algebraic

Does $k[X]$ always have a countable basis? ($X$ is an affine variety)

Question about motivation for upgrading varieties to schemes (nilpotency)

Projective variety $V_p(x^2 y - z^3)$ is singular

Definition of the Fibre of a Sheaf

Upper Semi-Continuity of the Rank of the Fibre of a Sheaf

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