User red_trumpet

9 votes

1 answer

2k views

Is the pull-back of the structure sheaf the structure sheaf?

asked Jan 18, 2019 at 8:18

9 votes

1 answer

210 views

Unexpected proof that $\alpha!$ divides $k!$ if $\alpha_1 + \dots + \alpha_n = k$.

asked Mar 4, 2019 at 12:39

9 votes

2 answers

225 views

Good argument that $\Omega_{X/k} = 0$ implies that $X$ is finite.

asked Jun 28, 2021 at 8:47

7 votes

1 answer

278 views

What exactly is a universal central extension?

asked May 24 at 11:28

7 votes

1 answer

811 views

Hartshorne Exercise III 3.2: $X$ is affine iff every component is affine

asked Apr 11, 2019 at 14:20

7 votes

1 answer

655 views

Is the natural map $f^* f_* \mathcal{F} \to \mathcal{F}$ surjective?

asked May 5, 2020 at 8:45

6 votes

1 answer

261 views

Why are meromorphic functions on a smooth projective curve rational?

asked Jul 19, 2022 at 12:03

5 votes

2 answers

448 views

Generic smoothness in the analytic setting.

asked Mar 5, 2021 at 8:08

5 votes

1 answer

222 views

Complexified bundle $\xi \otimes \mathbb{C}$ is isomorphic to its conjugate $\overline{\xi \otimes \mathbb{C}}$?

asked May 26, 2020 at 8:16

5 votes

0 answers

206 views

Regular differentials on a singular curve.

asked Oct 19, 2020 at 14:37

5 votes

1 answer

735 views

Hartshorne Exercise II 3.22 (a) - Dimensions of the Fibres of a morphism

asked Mar 4, 2020 at 14:11

5 votes

1 answer

910 views

Are open affine sets a base for the topology of a scheme?

asked Dec 15, 2017 at 13:18

5 votes

1 answer

545 views

Proof of Serre Duality in Hartshorne

asked Jul 3, 2018 at 9:09

5 votes

2 answers

989 views

Is a local ring Artinian, if the maximal ideal is nilpotent?

asked Jul 16, 2018 at 9:39

4 votes

1 answer

247 views

Ascending / descending chain condition on graded modules.

asked Oct 30, 2018 at 18:30

4 votes

1 answer

131 views

Openness of holomorphic maps

asked Sep 22, 2020 at 14:36

4 votes

1 answer

95 views

Dimension of linear system $|C|$ is the genus of $C$?

asked May 11, 2020 at 12:37

4 votes

1 answer

212 views

On a variety, every line bundle $L$ is isomorphic to $\mathcal{O}(D)$ for some Cartier divisor $D$?

asked Aug 10, 2020 at 13:43

4 votes

1 answer

71 views

What is the mathematically correct way to draw a sphere with great circles?

asked Apr 21, 2022 at 21:04

4 votes

1 answer

306 views

Local flatness criterion: A morphism $X \to Y$ of schemes over $S$ is flat if and only if it is flat on all fibers $X_s \to Y_s$, $s \in S$?

asked Nov 1, 2021 at 14:22

4 votes

1 answer

157 views

If the linear system $|2P_0|$ had base points, an elliptic curve would be rational?

asked Jan 6, 2022 at 16:10

4 votes

1 answer

70 views

When is the central singular fiber $X_0$ of a proper map $X \to D$ a deformation retract of $X$?

asked Oct 25 at 7:29

3 votes

1 answer

175 views

Are holomorphic structures on complex vector bundles unique up to isomorphism?

asked Aug 30, 2022 at 9:07

3 votes

3 answers

247 views

For an elliptic curve $E$, how can we describe canonical divisor or addition $\operatorname{Sym}^2(E) \to E$ as projectivization of a vector bundle?

asked Feb 8 at 14:48

3 votes

1 answer

173 views

Does a filtration of the irrational numbers become somewhere dense?

asked May 8 at 15:02

3 votes

1 answer

128 views

What is the motivation to study $\Gamma \backslash \mathbb H $, where $\Gamma \subset Sl_2(\mathbb Z)$ is a congruence subgroup?

asked May 15 at 8:59

3 votes

0 answers

52 views

When are calculations up to numerical equivalence appropriate?

asked Nov 22, 2021 at 19:54

3 votes

1 answer

231 views

$\partial \bar \partial$-lemma for $d$-exact differential form.

asked Jun 17, 2021 at 10:53

3 votes

0 answers

81 views

Can non-reduced fibers appear over a subset of codimension $\geq 2$?

asked Feb 7, 2021 at 21:07

3 votes

1 answer

435 views

Canonical morphism of dualizing sheaves under normalization.

asked Mar 16, 2021 at 10:31

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153 Questions

Is the pull-back of the structure sheaf the structure sheaf?

Unexpected proof that $\alpha!$ divides $k!$ if $\alpha_1 + \dots + \alpha_n = k$.

Good argument that $\Omega_{X/k} = 0$ implies that $X$ is finite.

What exactly is a universal central extension?

Hartshorne Exercise III 3.2: $X$ is affine iff every component is affine

Is the natural map $f^* f_* \mathcal{F} \to \mathcal{F}$ surjective?

Why are meromorphic functions on a smooth projective curve rational?

Generic smoothness in the analytic setting.

Complexified bundle $\xi \otimes \mathbb{C}$ is isomorphic to its conjugate $\overline{\xi \otimes \mathbb{C}}$?

Regular differentials on a singular curve.

Hartshorne Exercise II 3.22 (a) - Dimensions of the Fibres of a morphism

Are open affine sets a base for the topology of a scheme?

Proof of Serre Duality in Hartshorne

Is a local ring Artinian, if the maximal ideal is nilpotent?

Ascending / descending chain condition on graded modules.

Openness of holomorphic maps

Dimension of linear system $|C|$ is the genus of $C$?

On a variety, every line bundle $L$ is isomorphic to $\mathcal{O}(D)$ for some Cartier divisor $D$?

What is the mathematically correct way to draw a sphere with great circles?

Local flatness criterion: A morphism $X \to Y$ of schemes over $S$ is flat if and only if it is flat on all fibers $X_s \to Y_s$, $s \in S$?

If the linear system $|2P_0|$ had base points, an elliptic curve would be rational?

When is the central singular fiber $X_0$ of a proper map $X \to D$ a deformation retract of $X$?

Are holomorphic structures on complex vector bundles unique up to isomorphism?

For an elliptic curve $E$, how can we describe canonical divisor or addition $\operatorname{Sym}^2(E) \to E$ as projectivization of a vector bundle?

Does a filtration of the irrational numbers become somewhere dense?

What is the motivation to study $\Gamma \backslash \mathbb H $, where $\Gamma \subset Sl_2(\mathbb Z)$ is a congruence subgroup?

When are calculations up to numerical equivalence appropriate?

$\partial \bar \partial$-lemma for $d$-exact differential form.

Can non-reduced fibers appear over a subset of codimension $\geq 2$?

Canonical morphism of dualizing sheaves under normalization.