Question

Why introduce very ample sheaf and ample sheaf?

score 190 · Answer 1 · 2020-10-23 16:33:48

190

Views

Why introduce very ample sheaf and ample sheaf?

Published on 23 Oct 2020 - 16:33

score 68 · Answer 2 · 2020-10-24 14:03:47

68

Views

My attempt in Hartshorne's exercise II.1.21.(d)

Published on 24 Oct 2020 - 14:03

score 217 · Answer 3 · 2026-03-29 04:47:25

217

Views

What is the essential difference between a sheaf and a fibration with lifting property?

Published on 29 Mar 2026 - 4:47

score 102 · Answer 4 · 2020-10-26 11:25:54

102

Views

Finding the restriction maps of the image presheaf using the universal property

Published on 26 Oct 2020 - 11:25

score 99 · Answer 5 · 2020-10-26 15:02:25

99

Views

Showing that $\mathscr{F}(U\sqcup V)=\mathscr{F}(U)\times \mathscr{F}(V)$

Published on 26 Oct 2020 - 15:02

score 72 · Answer 6 · 2020-10-27 20:13:15

72

Views

Equivalence relation on the disjoint union of all sections of a presheaf - verify transitivity

Published on 27 Oct 2020 - 20:13

score 246 · Answer 7 · 2026-03-28 12:14:33

246

Views

Meaning of "cohomology" in algebraic geometry?

Published on 28 Mar 2026 - 12:14

score 95 · Answer 8 · 2020-10-31 11:49:50

95

Views

Difference between $\bigcup\mathscr{F}_x$ and $\mathscr{F}$

Published on 31 Oct 2020 - 11:49

score 554 · Answer 9 · 2026-03-26 01:02:59

554

Views

How to reduce to affine case to determine whether a given functor is representable

Published on 26 Mar 2026 - 1:02

score 126 · Answer 10 · 2026-03-26 23:11:33

126

Views

Example on coherent scheme but not noetherian, $\mathrm{Spec}\underset{n \in \mathbb{N}}{\cup}k[[t^{\frac{1}{n}}]]$.

Published on 26 Mar 2026 - 23:11

score 107 · Answer 11 · 2026-04-01 12:01:13

107

Views

full subcategory of $Fun(C,D)$ spanned by a collection of functors

Published on 01 Apr 2026 - 12:01

score 80 · Answer 12 · 2026-03-27 15:05:13

80

Views

Proposition 4.3 from "Mixed Hodge structures"

Published on 27 Mar 2026 - 15:05

score 467 · Answer 13 · 2026-03-27 05:41:47

467

Views

When can the sheaf cohomology of a quasi-coherent sheaf be computed in the category of quasi-coherent sheaves?

Published on 27 Mar 2026 - 5:41

score 50 · Answer 14 · 2020-11-10 16:05:34

50

Views

Example of not locally finitely generated sheaf

Published on 10 Nov 2020 - 16:05

score 145 · Answer 15 · 2026-02-23 12:24:27

145

Views

Is a module structure over a sheaf of rings the same as a module structure on each stalk?

Published on 23 Feb 2026 - 12:24

List Question

Why introduce very ample sheaf and ample sheaf?

My attempt in Hartshorne's exercise II.1.21.(d)

What is the essential difference between a sheaf and a fibration with lifting property?

Finding the restriction maps of the image presheaf using the universal property

Showing that $\mathscr{F}(U\sqcup V)=\mathscr{F}(U)\times \mathscr{F}(V)$

Equivalence relation on the disjoint union of all sections of a presheaf - verify transitivity

Meaning of "cohomology" in algebraic geometry?

Difference between $\bigcup\mathscr{F}_x$ and $\mathscr{F}$

How to reduce to affine case to determine whether a given functor is representable

Example on coherent scheme but not noetherian, $\mathrm{Spec}\underset{n \in \mathbb{N}}{\cup}k[[t^{\frac{1}{n}}]]$.

full subcategory of $Fun(C,D)$ spanned by a collection of functors

Proposition 4.3 from "Mixed Hodge structures"

When can the sheaf cohomology of a quasi-coherent sheaf be computed in the category of quasi-coherent sheaves?

Example of not locally finitely generated sheaf

Is a module structure over a sheaf of rings the same as a module structure on each stalk?

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