User Daniel

10 votes

2 answers

328 views

Finding an example of a degree 5 rational curve in $\mathbb{P}^3$ which is not in a quadric.

asked Mar 8, 2023 at 21:03

7 votes

0 answers

95 views

Is this property of flat morphisms accurate?

asked Sep 19, 2023 at 16:56

6 votes

0 answers

109 views

Find the kernel of $\mathbb{Z}[x] \to \mathbb{Q}$ given by $f \mapsto f(1/3)$.

asked Jul 5, 2022 at 17:28

6 votes

1 answer

127 views

Let $A$ be an integrally closed noetherian domain, and $(R, \mathfrak{m})$ local with $A \subseteq R \subseteq K(A)$. Is $R$ a localization of $A$?

asked Aug 10, 2021 at 22:06

6 votes

1 answer

701 views

What is the conormal sheaf?

asked Dec 17, 2021 at 0:19

5 votes

1 answer

517 views

Is the kernel of a surjective morphism $\mathscr{F} \to \mathscr{G}$ of locally free sheaves locally free?

asked Jan 1, 2022 at 23:29

5 votes

1 answer

95 views

Volume of the graded linear series $\Gamma_\bullet(\mathbf{P}^n, \mathcal{O}(1) \otimes \mathfrak{m}^c)$. Is it $1 - c$ or $1 - c^n$?

asked Sep 7, 2023 at 21:23

4 votes

1 answer

781 views

Finding $\operatorname{Aut}(X)$ where $X$ is the Fermat cubic surface in $\mathbb{P}^3$.

asked Jun 13, 2023 at 19:36

4 votes

0 answers

289 views

Why are degree zero line bundles on an Abelian Variety translation invariant?

asked May 7, 2022 at 20:41

4 votes

1 answer

786 views

Defining the natural almost complex structure on a complex manifold.

asked Aug 1, 2020 at 0:11

3 votes

2 answers

138 views

If $G$ is a group with $N$ normal and $H_1$, $H_2$ subgroups of $G$ with $H_1$ a normal subgroup of $H_2$, show $NH_1$ is a normal subgroup of $NH_2$.

asked Dec 6, 2020 at 22:30

3 votes

0 answers

55 views

$\newcommand{\Z}{\mathbb{Z}}$Let $R = \Z[x]$ and $I = (x)$, $J = (x, 7)$. Find $\operatorname{Tor}_i(R/I, R/J)$.

asked Jun 2, 2022 at 20:25

3 votes

1 answer

67 views

Is the connected assumption necessary in the following theorem?

asked Jun 2, 2022 at 20:49

3 votes

1 answer

132 views

Computation of $\operatorname{Tor}^{\mathbb{Q}[x,y]}_1(\mathbb{Q}[x,y]/(x,y), (x, y))$.

asked Aug 1, 2022 at 3:26

3 votes

1 answer

134 views

Why is $Z(y^2 - x^p - t)$ a regular scheme?

asked Nov 5, 2022 at 21:16

3 votes

0 answers

110 views

Confusion about cellular homology.

asked Apr 6, 2023 at 18:53

2 votes

1 answer

42 views

Let $G$ be a subgroup of $\mathbb{Q}^n$ with $\langle g, g' \rangle \in \mathbb{Z}$ for all $g, g' \in G$. Is $G$ finitely generated?

asked Mar 26, 2023 at 22:03

2 votes

1 answer

111 views

Defining a surjective map $\operatorname{Pic}(X \times X) \to \operatorname{End}(X, P_0)$ for an elliptic curve $X$

asked Feb 17, 2023 at 4:32

2 votes

1 answer

76 views

Is the map $\operatorname{Sym}^k(H^0(X, L)) \to H^0(X, L^k)$ injective, when $L$ is generated by global setions?

asked Aug 22, 2023 at 21:17

2 votes

1 answer

94 views

Induced extension of function fields for $k$-linear frobenius.

asked Dec 1, 2022 at 22:53

2 votes

1 answer

243 views

Filling the gaps in Hartshorne Proposition III.9.5.

asked Sep 20, 2022 at 3:45

2 votes

1 answer

82 views

Let $M = \operatorname{cok}(\phi)$ where $\phi: \mathbb{Z}^3 \to \mathbb{Z}^3$. Express $M$ as a direct sum of cyclic modules.

asked Jun 27, 2022 at 20:32

2 votes

2 answers

80 views

Let $A_i$ be measurable and $\sum_{i = 1}^\infty \mu (A_i)^2 < \infty$. Is $\mu( \bigcap_{ i = 1}^\infty \bigcup_{m = i}^\infty A_m) = 0$?

asked Jul 17, 2022 at 21:34

2 votes

0 answers

57 views

How can I use a 'rational section' to compute the Weil divisor associated to a line bundle?

asked Feb 15, 2022 at 19:36

2 votes

1 answer

123 views

Confusion about vanishing of ideal sheaves.

asked Mar 30, 2022 at 0:15

2 votes

0 answers

127 views

Can the union of an ascending sequence of ideals of $R$ be $R$?

asked Dec 22, 2020 at 0:48

2 votes

0 answers

84 views

If $A = \mathbb{Z}[\sqrt{-5}]$ and $I = (2, 1 + \sqrt{-5})$, why is $I \otimes_A I \cong A?$

asked Feb 23, 2021 at 16:55

2 votes

1 answer

83 views

If $f(z)$ is a nonconstant entire function that is not a polynomial, does $g(z) = f(1/z)$ have an essential singularity at 0?

asked Dec 3, 2019 at 4:05

2 votes

1 answer

164 views

Proof Verification: $\Omega_{X \times Y/S} \cong p_1^* \Omega_{X/S} \oplus p_2^* \Omega_{Y/S} $

asked Jan 6, 2022 at 19:28

2 votes

1 answer

105 views

Let $I \subset A$ be generated by a regular sequence $x_1, \dots, x_r$. Then, $I/I^2$ is a free $A/I$ module of rank $r$.

asked Dec 19, 2021 at 6:35

Stack Exchange Network

75 Questions

Finding an example of a degree 5 rational curve in $\mathbb{P}^3$ which is not in a quadric.

Is this property of flat morphisms accurate?

Find the kernel of $\mathbb{Z}[x] \to \mathbb{Q}$ given by $f \mapsto f(1/3)$.

Let $A$ be an integrally closed noetherian domain, and $(R, \mathfrak{m})$ local with $A \subseteq R \subseteq K(A)$. Is $R$ a localization of $A$?

What is the conormal sheaf?

Is the kernel of a surjective morphism $\mathscr{F} \to \mathscr{G}$ of locally free sheaves locally free?

Volume of the graded linear series $\Gamma_\bullet(\mathbf{P}^n, \mathcal{O}(1) \otimes \mathfrak{m}^c)$. Is it $1 - c$ or $1 - c^n$?

Finding $\operatorname{Aut}(X)$ where $X$ is the Fermat cubic surface in $\mathbb{P}^3$.

Why are degree zero line bundles on an Abelian Variety translation invariant?

Defining the natural almost complex structure on a complex manifold.

If $G$ is a group with $N$ normal and $H_1$, $H_2$ subgroups of $G$ with $H_1$ a normal subgroup of $H_2$, show $NH_1$ is a normal subgroup of $NH_2$.

$\newcommand{\Z}{\mathbb{Z}}$Let $R = \Z[x]$ and $I = (x)$, $J = (x, 7)$. Find $\operatorname{Tor}_i(R/I, R/J)$.

Is the connected assumption necessary in the following theorem?

Computation of $\operatorname{Tor}^{\mathbb{Q}[x,y]}_1(\mathbb{Q}[x,y]/(x,y), (x, y))$.

Why is $Z(y^2 - x^p - t)$ a regular scheme?

Confusion about cellular homology.

Let $G$ be a subgroup of $\mathbb{Q}^n$ with $\langle g, g' \rangle \in \mathbb{Z}$ for all $g, g' \in G$. Is $G$ finitely generated?

Defining a surjective map $\operatorname{Pic}(X \times X) \to \operatorname{End}(X, P_0)$ for an elliptic curve $X$

Is the map $\operatorname{Sym}^k(H^0(X, L)) \to H^0(X, L^k)$ injective, when $L$ is generated by global setions?

Induced extension of function fields for $k$-linear frobenius.

Filling the gaps in Hartshorne Proposition III.9.5.

Let $M = \operatorname{cok}(\phi)$ where $\phi: \mathbb{Z}^3 \to \mathbb{Z}^3$. Express $M$ as a direct sum of cyclic modules.

Let $A_i$ be measurable and $\sum_{i = 1}^\infty \mu (A_i)^2 < \infty$. Is $\mu( \bigcap_{ i = 1}^\infty \bigcup_{m = i}^\infty A_m) = 0$?

How can I use a 'rational section' to compute the Weil divisor associated to a line bundle?

Confusion about vanishing of ideal sheaves.

Can the union of an ascending sequence of ideals of $R$ be $R$?

If $A = \mathbb{Z}[\sqrt{-5}]$ and $I = (2, 1 + \sqrt{-5})$, why is $I \otimes_A I \cong A?$

If $f(z)$ is a nonconstant entire function that is not a polynomial, does $g(z) = f(1/z)$ have an essential singularity at 0?

Proof Verification: $\Omega_{X \times Y/S} \cong p_1^* \Omega_{X/S} \oplus p_2^* \Omega_{Y/S} $

Let $I \subset A$ be generated by a regular sequence $x_1, \dots, x_r$. Then, $I/I^2$ is a free $A/I$ module of rank $r$.