Question

About the definition of the morphisms of varieties in Hartshorne's algebraic geometry.

score 121 · Answer 1 · 2026-03-25 22:05:06

121

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About the definition of the morphisms of varieties in Hartshorne's algebraic geometry.

Published on 25 Mar 2026 - 22:05

score 50 · Answer 2 · 2023-03-24 15:44:52

50

Views

The limit in affine (projective) space.

Published on 24 Mar 2023 - 15:44

score 35 · Answer 3 · 2023-03-29 02:20:11

35

Views

For $f \in K[x_0,\ldots,x_n]$ then, $(\phi_i^{-1})^(\phi_i^(f)) | f$

Published on 29 Mar 2023 - 2:20

score 133 · Answer 4 · 2023-03-30 08:26:25

133

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rank of jacobian matrix of generators of ideal of affine variety is the dimension as a subspace of k^n

Published on 30 Mar 2023 - 8:26

score 62 · Answer 5 · 2023-04-03 20:46:33

62

Views

Qing Liu Proposition 2.5.5, $\dim X=\sup\{\dim_x X \mid x \in X\}$

Published on 03 Apr 2023 - 20:46

score 35 · Answer 6 · 2026-03-25 19:10:28

35

Views

Smoothness of affine variety consisting of finitely many points

Published on 25 Mar 2026 - 19:10

score 64 · Answer 7 · 2026-03-25 07:45:42

64

Views

Intuitive reason for why $\operatorname{Spec}(k[x,y,z]/(x-yz))$ is smooth at $O$ while $\operatorname{Spec}(k[x,y,z]/(x^2-yz))$ isn't?

Published on 25 Mar 2026 - 7:45

score 573 · Answer 8 · 2023-04-14 15:44:50

573

Views

Definition of 'gluing two affine curves'

Published on 14 Apr 2023 - 15:44

score 45 · Answer 9 · 2023-04-15 16:49:35

45

Views

How is the product of abstract affine varieties defined?

Published on 15 Apr 2023 - 16:49

score 121 · Answer 10 · 2026-02-23 05:13:26

121

Views

Subvarieties of an abstract affine variety

Published on 23 Feb 2026 - 5:13

score 53 · Answer 11 · 2023-04-18 11:46:17

53

Views

Dimension of an algebraic variety defined by two polynomials

Published on 18 Apr 2023 - 11:46

score 58 · Answer 12 · 2023-04-22 09:25:36

58

Views

regular functions on distinguished open sets in affine space

Published on 22 Apr 2023 - 9:25

score 88 · Answer 13 · 2023-04-25 19:52:33

88

Views

$\mathscr{O}_X(X-Y)=\mathbb{K}[X]$ if and only if $\text{codim}_X(Y)\geq 2$

Published on 25 Apr 2023 - 19:52

score 128 · Answer 14 · 2023-04-27 19:11:41

128

Views

$\mathbb Z$-graded coordinate ring $\iff$ $\mathbb C^*$ action on affine variety

Published on 27 Apr 2023 - 19:11

score 103 · Answer 15 · 2023-04-27 22:35:40

103

Views

Extending a map $\mathbb{A}^1-\{0\}\to \mathbb{P}^1$

Published on 27 Apr 2023 - 22:35

List Question

About the definition of the morphisms of varieties in Hartshorne's algebraic geometry.

The limit in affine (projective) space.

For $f \in K[x_0,\ldots,x_n]$ then, $(\phi_i^{-1})^(\phi_i^(f)) | f$

rank of jacobian matrix of generators of ideal of affine variety is the dimension as a subspace of k^n

Qing Liu Proposition 2.5.5, $\dim X=\sup\{\dim_x X \mid x \in X\}$

Smoothness of affine variety consisting of finitely many points

Intuitive reason for why $\operatorname{Spec}(k[x,y,z]/(x-yz))$ is smooth at $O$ while $\operatorname{Spec}(k[x,y,z]/(x^2-yz))$ isn't?

Definition of 'gluing two affine curves'

How is the product of abstract affine varieties defined?

Subvarieties of an abstract affine variety

Dimension of an algebraic variety defined by two polynomials

regular functions on distinguished open sets in affine space

$\mathscr{O}_X(X-Y)=\mathbb{K}[X]$ if and only if $\text{codim}_X(Y)\geq 2$

$\mathbb Z$-graded coordinate ring $\iff$ $\mathbb C^*$ action on affine variety

Extending a map $\mathbb{A}^1-\{0\}\to \mathbb{P}^1$

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