Question

Fibers of Spec maps: is $\operatorname{Spec} \Bbb C[x,y]/(x^3+x^2y+xy^2)\to\operatorname{Spec} \Bbb C[x]$ finite?

score 116 · Answer 1 · 2023-02-19 15:02:10

116

Views

Fibers of Spec maps: is $\operatorname{Spec} \Bbb C[x,y]/(x^3+x^2y+xy^2)\to\operatorname{Spec} \Bbb C[x]$ finite?

Published on 19 Feb 2023 - 15:02

score 32 · Answer 2 · 2023-04-19 10:59:56

32

Views

Restriction of a morphism to the inverse image of a closed set

Published on 19 Apr 2023 - 10:59

score 39 · Answer 3 · 2023-06-01 10:32:44

39

Views

Surfaces with $p_g=q=0$ and $Pic$ generated by rational curves are rational?

Published on 01 Jun 2023 - 10:32

score 67 · Answer 4 · 2023-07-31 19:49:46

67

Views

Isomorphic affine classical varieties over a non-algebraically closed field. Does the isomorphism preserve polynomials?

Published on 31 Jul 2023 - 19:49

score 101 · Answer 5 · 2023-10-07 17:06:37

101

Views

Dimension of the Zariski closure of certain subset of matrices

Published on 07 Oct 2023 - 17:06

score 41 · Answer 6 · 2023-11-15 16:55:26

41

Views

Local equation of a line near a point in a cone

Published on 15 Nov 2023 - 16:55

score 183 · Answer 7 · 2023-11-24 08:28:06

183

Views

How to do concrete calculations in algebraic geometry?

Published on 24 Nov 2023 - 8:28

score 214 · Answer 8 · 2023-11-27 06:05:34

214

Views

How do I translate the intersection of two affine curves in a plane into a statement about ideals in $k[X, Y]$?

Published on 27 Nov 2023 - 6:05

score 118 · Answer 9 · 2023-11-28 13:26:14

118

Views

Is $\mathbb{C}^{n+1}$ \ $\{0\}$ isomorphic to $\mathbb{P}^n\times \mathbb{C}^*$?

Published on 28 Nov 2023 - 13:26

score 72 · Answer 10 · 2023-12-07 08:22:30

72

Views

Can the intersection multiplicity for plane curves be defined computationally?

Published on 07 Dec 2023 - 8:22

score 35 · Answer 11 · 2024-01-18 20:32:38

35

Views

Dimension of image of projective space

Published on 18 Jan 2024 - 20:32

score 68 · Answer 12 · 2024-01-21 07:43:18

68

Views

Do two lines passing through two (not necessarily distinct) points on an irred. cubic necessarily coincide? (Proof of Sec. 5.6, Prop. 3 in Fulton)

Published on 21 Jan 2024 - 7:43

score 52 · Answer 13 · 2024-01-22 23:15:13

52

Views

Does Fulton's proof of Cayley-Bacharach Theorem (two cubics that intersect a third cubic in 8 points share the 9th) require proof by contradiction?

Published on 22 Jan 2024 - 23:15

score 194 · Answer 14 · 2023-01-27 12:19:55

194

Views

Is a morphism from a quasi-affine variety to a quasi-projective variety given by globally defined regular maps?

Published on 27 Jan 2023 - 12:19

List Question

Fibers of Spec maps: is $\operatorname{Spec} \Bbb C[x,y]/(x^3+x^2y+xy^2)\to\operatorname{Spec} \Bbb C[x]$ finite?

Restriction of a morphism to the inverse image of a closed set

Surfaces with $p_g=q=0$ and $Pic$ generated by rational curves are rational?

Isomorphic affine classical varieties over a non-algebraically closed field. Does the isomorphism preserve polynomials?

Dimension of the Zariski closure of certain subset of matrices

Local equation of a line near a point in a cone

How to do concrete calculations in algebraic geometry?

How do I translate the intersection of two affine curves in a plane into a statement about ideals in $k[X, Y]$?

Is $\mathbb{C}^{n+1}$ \ $\{0\}$ isomorphic to $\mathbb{P}^n\times \mathbb{C}^*$?

Can the intersection multiplicity for plane curves be defined computationally?

Dimension of image of projective space

Do two lines passing through two (not necessarily distinct) points on an irred. cubic necessarily coincide? (Proof of Sec. 5.6, Prop. 3 in Fulton)

Does Fulton's proof of Cayley-Bacharach Theorem (two cubics that intersect a third cubic in 8 points share the 9th) require proof by contradiction?

Is a morphism from a quasi-affine variety to a quasi-projective variety given by globally defined regular maps?

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