List questions from affine-varieties

Published on 01 Oct 2019 - 6:26

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For which $n$ is $\mathbb{A}^n\setminus \{0\}$ an affine variety?

Published on 28 Jul 2014 - 20:49

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Problem in proving that $\mathbb{A}^2$ is not homeomorphic to $\mathbb{P}^2$

Published on 25 Mar 2026 - 7:41

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Is the sheaf of differentials of a smooth morphism locally free?

Published on 02 Oct 2019 - 10:10

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Affine Varieties

Published on 24 Mar 2026 - 0:17

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Can a singular variety $V(f)\subset \bar{k}^2$ be nonsingular on $V(f)\cap k^2\neq \emptyset$?

Published on 03 Oct 2019 - 15:53

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Example 1.23 of Shafarevich's book.

Published on 04 Oct 2019 - 0:50

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More confusion about the definition of smooth morphisms of schemes

Published on 26 Feb 2026 - 13:46

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Regular Functions and Coordinate Rings

Published on 06 Oct 2019 - 23:06

358

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How many irreducible components can an affine algebraic set have?

Published on 09 Oct 2019 - 8:42

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Decomposition of ideal into intersection of prime ideals

Published on 09 Oct 2019 - 19:12

852

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Closed subset of a variety is also a variety

Published on 09 Oct 2019 - 21:13

249

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What is the ring defining the intersection of two open affines in a variety?

Published on 20 Mar 2026 - 10:29

329

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Morphism between a variety and a closed subvariety

Published on 17 Mar 2026 - 2:06

739

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Affine Algebraic Sets: Open and Closed Sets?

Published on 25 Mar 2026 - 13:51

List Question

Tangent and cotangent spaces of varieties over a field

For which $n$ is $\mathbb{A}^n\setminus \{0\}$ an affine variety?

Problem in proving that $\mathbb{A}^2$ is not homeomorphic to $\mathbb{P}^2$

Is the sheaf of differentials of a smooth morphism locally free?

Affine Varieties

Can a singular variety $V(f)\subset \bar{k}^2$ be nonsingular on $V(f)\cap k^2\neq \emptyset$?

Example 1.23 of Shafarevich's book.

More confusion about the definition of smooth morphisms of schemes

Regular Functions and Coordinate Rings

How many irreducible components can an affine algebraic set have?

Decomposition of ideal into intersection of prime ideals

Closed subset of a variety is also a variety

What is the ring defining the intersection of two open affines in a variety?

Morphism between a variety and a closed subvariety

Affine Algebraic Sets: Open and Closed Sets?

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