List questions from affine-varieties

Published on 03 Jun 2018 - 18:24

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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 08 Jun 2018 - 10:45

50

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

Published on 08 Jun 2018 - 11:38

60

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Nonsingular points go to nonsingular points?

Published on 12 Jun 2018 - 14:05

460

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Underlying variety of $\mathbb{G}_m$

Published on 22 Mar 2026 - 9:25

396

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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 17 Jun 2018 - 21:37

203

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

Published on 29 Jun 2018 - 13:53

71

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How can I show that irreducibility for this set?

Published on 29 Jun 2018 - 16:21

539

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

Published on 01 Jul 2018 - 10:40

200

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Local ring of a smooth subvariety.

Published on 06 Jul 2018 - 11:18

440

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Action of torus on an affine toric variety

Published on 16 Jul 2018 - 6:29

82

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Question about meaning behind a map of schemes

Published on 01 Aug 2018 - 18:59

1.6k

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Proof of Theorem of Dimension of Fibres

Published on 22 Mar 2026 - 16:00

775

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Irreducible affine algebraic varieties corresponds to prime ideals

Published on 06 Aug 2018 - 18:22

72

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Affine algebraic varieties associated with arbitrary sets

Published on 12 Aug 2018 - 15:28

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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