List questions from affine-varieties

Published on 20 Oct 2023 - 18:40

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Find $\dim_k(m/m^2)$ in a local ring without geometric interpretation.

Published on 23 Oct 2023 - 8:34

35

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Varieties with parameters

Published on 25 Mar 2026 - 13:51

90

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how to prove that a set is not algebraic

Published on 26 Mar 2026 - 1:03

109

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Tangent space of a quotient of an algebraic variety

Published on 02 Nov 2023 - 11:42

49

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The plane in the quadric 3-fold is not a (set-theoretic) hypersurface

Published on 25 Mar 2026 - 4:41

42

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$\tilde f_i = f_i + g_i$, then $\dim \mathbb C[t_1,\dots, t_d]/\langle f_i \rangle \leq \dim \mathbb C[t_1,\dots,t_d]/ \langle \tilde f_i \rangle$

Published on 25 Mar 2026 - 18:50

24

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How to prove that $\phi (x,\frac{1}{x}) = x$ and $ \psi( x) = (x,\frac{1}{x}) $ are morphisms of varieties?

Published on 07 Nov 2023 - 15:20

46

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

Published on 26 Mar 2026 - 1:03

38

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Maximal ideal of a point is principal

Published on 18 Nov 2023 - 14:34

49

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Simpler way to express the affine variety V(f, g, h) in terms of union and intersection of varieties

Published on 27 Nov 2023 - 10:12

284

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Why is the noetherian ring property not definable in first-order logic?

Published on 03 Dec 2023 - 11:21

62

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Confusion about $k$-algebra homomorphisms from $k[W] \to k[V]$.

Published on 06 Dec 2023 - 4:38

24

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Existence of function in coordinate ring vanishing at a point

Published on 12 Dec 2023 - 9:38

96

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Show product of projective spaces minus a hypersurface is affine

Published on 13 Dec 2023 - 0:10

List Question

Algebraic tangent space of image of a morphism

Find $\dim_k(m/m^2)$ in a local ring without geometric interpretation.

Varieties with parameters

how to prove that a set is not algebraic

Tangent space of a quotient of an algebraic variety

The plane in the quadric 3-fold is not a (set-theoretic) hypersurface

$\tilde f_i = f_i + g_i$, then $\dim \mathbb C[t_1,\dots, t_d]/\langle f_i \rangle \leq \dim \mathbb C[t_1,\dots,t_d]/ \langle \tilde f_i \rangle$

How to prove that $\phi (x,\frac{1}{x}) = x$ and $ \psi( x) = (x,\frac{1}{x}) $ are morphisms of varieties?

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

Maximal ideal of a point is principal

Simpler way to express the affine variety V(f, g, h) in terms of union and intersection of varieties

Why is the noetherian ring property not definable in first-order logic?

Confusion about $k$-algebra homomorphisms from $k[W] \to k[V]$.

Existence of function in coordinate ring vanishing at a point

Show product of projective spaces minus a hypersurface is affine

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