Question

For $D$ very ample on a threefold $X$, is it true that $D^2.S\geq(\operatorname{mult}_x D)^2\cdot\operatorname{mult}_x S$?

score 26 · Answer 1 · 2023-08-16 07:36:04

26

Views

For $D$ very ample on a threefold $X$, is it true that $D^2.S\geq(\operatorname{mult}_x D)^2\cdot\operatorname{mult}_x S$?

Published on 16 Aug 2023 - 7:36

score 38 · Answer 2 · 2023-08-18 11:04:31

38

Views

Does Kleiman's Theorem work on quasi-projective varieties?

Published on 18 Aug 2023 - 11:04

score 49 · Answer 3 · 2023-09-11 12:36:18

49

Views

Intuition of projective line via glueing

Published on 11 Sep 2023 - 12:36

score 45 · Answer 4 · 2023-09-15 07:11:32

45

Views

Vanishing ideal of a subset of $\operatorname{Proj} S_\bullet$

Published on 15 Sep 2023 - 7:11

score 23 · Answer 5 · 2023-10-10 14:13:05

23

Views

Example of a family of ample divisors $\{A_m\}_{m\geq 1}$ on a smooth projective variety $X$ such that $mA_m$ has a basepoint?

Published on 10 Oct 2023 - 14:13

score 40 · Answer 6 · 2023-10-11 06:07:35

40

Views

global section of a B-scheme defines a morphism to projective $B$-scheme

Published on 11 Oct 2023 - 6:07

score 64 · Answer 7 · 2023-10-25 07:37:43

64

Views

Problem showing the saturation map of a graded ring f.g. in degree 1 induces an isomorphism of projective schemes and O(1) (The Rising Sea 15.6.G)

Published on 25 Oct 2023 - 7:37

score 83 · Answer 8 · 2026-03-24 20:46:12

83

Views

What is $k((t))$?

Published on 24 Mar 2026 - 20:46

score 44 · Answer 9 · 2023-11-17 15:29:30

44

Views

Morphism of schemes and closed points

Published on 17 Nov 2023 - 15:29

score 71 · Answer 10 · 2023-11-20 04:48:16

71

Views

image of Segre embedding is cut out (scheme-theoretically) by vanishing minors

Published on 20 Nov 2023 - 4:48

score 124 · Answer 11 · 2023-12-17 20:14:21

124

Views

Effective divisors of $X$ with $\operatorname{Pic}X\cong \mathbb Z$

Published on 17 Dec 2023 - 20:14

score 48 · Answer 12 · 2024-01-10 10:53:30

48

Views

Is projective morphism over a discrete valuation ring always flat?

Published on 10 Jan 2024 - 10:53

score 92 · Answer 13 · 2024-01-10 11:45:17

92

Views

[Cor 5.3.24 in Qing Liu]If $X$ is a projective scheme over a DVR $A$, then any coherent sheaf of ideal of $\mathcal{O}_X$ is flat over $A$?

Published on 10 Jan 2024 - 11:45

score 55 · Answer 14 · 2024-01-13 09:44:06

55

Views

Reduced, irreducible and integral schemes

Published on 13 Jan 2024 - 9:44

score 77 · Answer 15 · 2024-01-16 10:09:26

77

Views

Inverse image of a $0$-dimensional subscheme under a finite morphism

Published on 16 Jan 2024 - 10:09

List Question

For $D$ very ample on a threefold $X$, is it true that $D^2.S\geq(\operatorname{mult}_x D)^2\cdot\operatorname{mult}_x S$?

Does Kleiman's Theorem work on quasi-projective varieties?

Intuition of projective line via glueing

Vanishing ideal of a subset of $\operatorname{Proj} S_\bullet$

Example of a family of ample divisors $\{A_m\}_{m\geq 1}$ on a smooth projective variety $X$ such that $mA_m$ has a basepoint?

global section of a B-scheme defines a morphism to projective $B$-scheme

Problem showing the saturation map of a graded ring f.g. in degree 1 induces an isomorphism of projective schemes and O(1) (The Rising Sea 15.6.G)

What is $k((t))$?

Morphism of schemes and closed points

image of Segre embedding is cut out (scheme-theoretically) by vanishing minors

Effective divisors of $X$ with $\operatorname{Pic}X\cong \mathbb Z$

Is projective morphism over a discrete valuation ring always flat?

[Cor 5.3.24 in Qing Liu]If $X$ is a projective scheme over a DVR $A$, then any coherent sheaf of ideal of $\mathcal{O}_X$ is flat over $A$?

Reduced, irreducible and integral schemes

Inverse image of a $0$-dimensional subscheme under a finite morphism

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