Question

Which is canonical $|D|\cong \mathbb{P}(\Gamma(X,\mathscr{O}_X(D))^{\vee}$) or $|D|\cong \mathbb{P}(\Gamma(X,\mathscr{O}_X(D))$)?

score 83 · Answer 1 · 2021-02-03 12:54:15

83

Views

Which is canonical $|D|\cong \mathbb{P}(\Gamma(X,\mathscr{O}_X(D))^{\vee}$) or $|D|\cong \mathbb{P}(\Gamma(X,\mathscr{O}_X(D))$)?

Published on 03 Feb 2021 - 12:54

score 105 · Answer 2 · 2021-02-03 20:06:47

105

Views

The complement of a neighborhood of a divisor.

Published on 03 Feb 2021 - 20:06

score 30 · Answer 3 · 2021-02-04 08:38:01

30

Views

How to devide an linear object to calculate how many of transverse smaller objects would be there and to be simetrical

Published on 04 Feb 2021 - 8:38

score 43 · Answer 4 · 2021-02-27 17:11:47

43

Views

Pullback of a pencil on a smooth surface with irreducible fibers is injective

Published on 27 Feb 2021 - 17:11

score 39 · Answer 5 · 2021-03-02 07:42:54

39

Views

Does a curve $C \subset X$ that contains a singularity of $X$ pick up extra multiplicities?

Published on 02 Mar 2021 - 7:42

score 309 · Answer 6 · 2021-03-04 21:28:33

309

Views

Vakil 14.2 isomorphism of the pair (invertible sheaf, rational section)

Published on 04 Mar 2021 - 21:28

score 98 · Answer 7 · 2021-03-06 10:13:14

98

Views

What is the rational function associated to a dominant morphism to $\mathbb{P}^1$?

Published on 06 Mar 2021 - 10:13

score 64 · Answer 8 · 2021-03-06 18:20:19

64

Views

Confusion about canonical rational section of the sheaf of a divisor

Published on 06 Mar 2021 - 18:20

score 315 · Answer 9 · 2021-03-10 06:39:15

315

Views

Divisor class group $\text{Cl}(X\times\mathbb{P}^n_k)\cong \text{Cl}(X)\times \mathbb{Z}$

Published on 10 Mar 2021 - 6:39

score 73 · Answer 10 · 2021-03-11 06:24:41

73

Views

Picard number of a blown up quadric

Published on 11 Mar 2021 - 6:24

score 130 · Answer 11 · 2021-03-15 15:59:00

130

Views

Proving a sheaf is not locally free

Published on 15 Mar 2021 - 15:59

score 211 · Answer 12 · 2021-03-15 18:51:59

211

Views

Uniformiser in book by Miranda

Published on 15 Mar 2021 - 18:51

score 55 · Answer 13 · 2021-03-24 15:21:45

55

Views

If $D$ is nef, then $h^1(D)=h^2(D)=0$

Published on 24 Mar 2021 - 15:21

score 191 · Answer 14 · 2026-03-26 09:16:21

191

Views

Showing $f_*\mathcal{O}_Y(E) = \mathcal{O}_X$ if and only if $E$ is effective.

Published on 26 Mar 2026 - 9:16

score 64 · Answer 15 · 2021-03-27 08:35:39

64

Views

What are the divisors $P,2P,3P,...$?

Published on 27 Mar 2021 - 8:35

List Question

Which is canonical $|D|\cong \mathbb{P}(\Gamma(X,\mathscr{O}_X(D))^{\vee}$) or $|D|\cong \mathbb{P}(\Gamma(X,\mathscr{O}_X(D))$)?

The complement of a neighborhood of a divisor.

How to devide an linear object to calculate how many of transverse smaller objects would be there and to be simetrical

Pullback of a pencil on a smooth surface with irreducible fibers is injective

Does a curve $C \subset X$ that contains a singularity of $X$ pick up extra multiplicities?

Vakil 14.2 isomorphism of the pair (invertible sheaf, rational section)

What is the rational function associated to a dominant morphism to $\mathbb{P}^1$?

Confusion about canonical rational section of the sheaf of a divisor

Divisor class group $\text{Cl}(X\times\mathbb{P}^n_k)\cong \text{Cl}(X)\times \mathbb{Z}$

Picard number of a blown up quadric

Proving a sheaf is not locally free

Uniformiser in book by Miranda

If $D$ is nef, then $h^1(D)=h^2(D)=0$

Showing $f_*\mathcal{O}_Y(E) = \mathcal{O}_X$ if and only if $E$ is effective.

What are the divisors $P,2P,3P,...$?

Trending Questions

Popular # Hahtags

Popular Questions