Question

Finitely generated $k-$algebras of regular functions on an algebraic variety

score 268 · Answer 1 · 2026-03-17 13:19:56

268

Views

Finitely generated $k-$algebras of regular functions on an algebraic variety

Published on 17 Mar 2026 - 13:19

score 143 · Answer 2 · 2026-03-17 12:05:09

143

Views

Is every open affine subscheme of an algebraic $k-$variety an affine $k-$variety?

Published on 17 Mar 2026 - 12:05

score 28 · Answer 3 · 2026-03-20 07:37:43

28

Views

Let $f(x, y) = y^2 - g(x) \in \mathbb{R}[x, y]$. Show that $(0, 0)$ is a singular point if and only if $g(x) = x^2(x-a)$.

Published on 20 Mar 2026 - 7:37

score 676 · Answer 4 · 2026-03-20 18:35:01

676

Views

Show that the ideal $(XY+XZ+YZ,XYZ) = (X,Y)(Y,Z)(X,Z)$ and the irreducibility of the vanishing sets of the factors.

Published on 20 Mar 2026 - 18:35

score 1k · Answer 5 · 2026-03-20 11:52:27

1k

Views

The 1-affine space is not isomorphic to the 1-affine space minus one point

Published on 20 Mar 2026 - 11:52

score 132 · Answer 6 · 2026-03-22 08:13:54

132

Views

Proving $\mathcal V(\mathcal I(A)) =A$ and $\mathcal I(\mathcal V(B))= \sqrt{B} $

Published on 22 Mar 2026 - 8:13

score 981 · Answer 7 · 2026-03-20 02:08:16

981

Views

Connectedness and path connectedness, of irreducible affine algebraic set in $\mathbb C^n$, under usual Euclidean topology

Published on 20 Mar 2026 - 2:08

score 440 · Answer 8 · 2026-03-20 03:49:09

440

Views

Is the complement of a complex affine algebraic set in an irreducible complex affine algebraic set (path) connected in the euclidean topology?

Published on 20 Mar 2026 - 3:49

score 320 · Answer 9 · 2026-03-20 06:30:39

320

Views

Does an irreducible real affine algebraic set/ its complement has finitely many connected components in the Euclidean topology?

Published on 20 Mar 2026 - 6:30

score 506 · Answer 10 · 2026-03-20 08:58:19

506

Views

On the radical of an ideal in the polynomial ring in 4 variables over complex field

Published on 20 Mar 2026 - 8:58

score 367 · Answer 11 · 2026-03-20 08:45:37

367

Views

Describe the corresponding $k$-algebra homomorphism $\tilde{\varphi}:k[V]\to k[\mathbb{A}^1]$.

Published on 20 Mar 2026 - 8:45

score 886 · Answer 12 · 2026-03-19 23:24:49

886

Views

Restriction of a morphism is a morphism

Published on 19 Mar 2026 - 23:24

score 239 · Answer 13 · 2026-03-22 11:28:52

239

Views

Affine neighbourhood containing two given points

Published on 22 Mar 2026 - 11:28

score 1.2k · Answer 14 · 2026-03-22 11:46:53

1.2k

Views

Is a bijective morphism between affine varieties an isomorphism?

Published on 22 Mar 2026 - 11:46

score 57 · Answer 15 · 2026-03-24 10:46:04

57

Views

Projective Variety of a Quadric is Tangent to x=0

Published on 24 Mar 2026 - 10:46

List Question

Finitely generated $k-$algebras of regular functions on an algebraic variety

Is every open affine subscheme of an algebraic $k-$variety an affine $k-$variety?

Let $f(x, y) = y^2 - g(x) \in \mathbb{R}[x, y]$. Show that $(0, 0)$ is a singular point if and only if $g(x) = x^2(x-a)$.

Show that the ideal $(XY+XZ+YZ,XYZ) = (X,Y)(Y,Z)(X,Z)$ and the irreducibility of the vanishing sets of the factors.

The 1-affine space is not isomorphic to the 1-affine space minus one point

Proving $\mathcal V(\mathcal I(A)) =A$ and $\mathcal I(\mathcal V(B))= \sqrt{B} $

Connectedness and path connectedness, of irreducible affine algebraic set in $\mathbb C^n$, under usual Euclidean topology

Is the complement of a complex affine algebraic set in an irreducible complex affine algebraic set (path) connected in the euclidean topology?

Does an irreducible real affine algebraic set/ its complement has finitely many connected components in the Euclidean topology?

On the radical of an ideal in the polynomial ring in 4 variables over complex field

Describe the corresponding $k$-algebra homomorphism $\tilde{\varphi}:k[V]\to k[\mathbb{A}^1]$.

Restriction of a morphism is a morphism

Affine neighbourhood containing two given points

Is a bijective morphism between affine varieties an isomorphism?

Projective Variety of a Quadric is Tangent to x=0

Trending Questions

Popular # Hahtags

Popular Questions