List questions from affine-varieties

Published on 16 Apr 2026 - 21:18

80

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Does there exist $m\ne n$ such that some open subset of $\mathbb A^m_k$ is homeomorphic with some open subset of $\mathbb A^n_k$?

Published on 15 Apr 2026 - 11:58

54

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Description of irreducible closed subsets of $\mathbb A^m_k \times \mathbb A^n_k$

Published on 10 May 2026 - 13:50

63

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Nonsingular points go to nonsingular points?

Published on 13 Apr 2026 - 14:21

463

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Underlying variety of $\mathbb{G}_m$

Published on 16 Apr 2026 - 6:14

399

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Let $X$ be an affine variety and U ⊆ X a dense open set. Then dim X \ U < dim X.

Published on 16 Apr 2026 - 12:33

206

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Ring of functions is finitely generated in a quasi compact variety.

Published on 12 Apr 2026 - 12:47

74

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How can I show that irreducibility for this set?

Published on 13 Apr 2026 - 7:35

542

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Let $i: X \to Y$ be the inclusion of a closed subvariety. Then $i$ is a finite morphism

Published on 14 Apr 2026 - 14:54

205

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Local ring of a smooth subvariety.

Published on 14 Apr 2026 - 20:39

443

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Action of torus on an affine toric variety

Published on 16 Apr 2026 - 6:59

86

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Question about meaning behind a map of schemes

Published on 09 Apr 2026 - 14:27

1.6k

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Proof of Theorem of Dimension of Fibres

Published on 05 May 2026 - 14:56

777

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Irreducible affine algebraic varieties corresponds to prime ideals

Published on 14 Apr 2026 - 6:35

75

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Affine algebraic varieties associated with arbitrary sets

Published on 15 Apr 2026 - 10:48

List Question

Functor from the category of varieties to the category of schemes.

Does there exist $m\ne n$ such that some open subset of $\mathbb A^m_k$ is homeomorphic with some open subset of $\mathbb A^n_k$?

Description of irreducible closed subsets of $\mathbb A^m_k \times \mathbb A^n_k$

Nonsingular points go to nonsingular points?

Underlying variety of $\mathbb{G}_m$

Let $X$ be an affine variety and U ⊆ X a dense open set. Then dim X \ U < dim X.

Ring of functions is finitely generated in a quasi compact variety.

How can I show that irreducibility for this set?

Let $i: X \to Y$ be the inclusion of a closed subvariety. Then $i$ is a finite morphism

Local ring of a smooth subvariety.

Action of torus on an affine toric variety

Question about meaning behind a map of schemes

Proof of Theorem of Dimension of Fibres

Irreducible affine algebraic varieties corresponds to prime ideals

Affine algebraic varieties associated with arbitrary sets

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