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Daniel
  • Member for 7 years, 4 months
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10 votes
2 answers
306 views

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

7 votes
0 answers
94 views

Is this property of flat morphisms accurate?

6 votes
0 answers
106 views

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

6 votes
1 answer
125 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 $A$?

6 votes
1 answer
629 views

What is the conormal sheaf?

5 votes
1 answer
482 views

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

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 $1 - c^n$?

4 votes
1 answer
645 views

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

4 votes
0 answers
270 views

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

4 votes
1 answer
693 views

Defining the natural almost complex structure on a complex manifold.

3 votes
2 answers
134 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 $NH_2$.

3 votes
0 answers
55 views

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

3 votes
1 answer
67 views

Is the connected assumption necessary in the following theorem?

3 votes
1 answer
130 views

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

3 votes
1 answer
130 views

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

3 votes
0 answers
99 views

Confusion about cellular homology.

2 votes
1 answer
40 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?

2 votes
1 answer
107 views

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

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?

2 votes
1 answer
86 views

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

2 votes
1 answer
225 views

Filling the gaps in Hartshorne Proposition III.9.5.

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.

2 votes
2 answers
79 views

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

2 votes
0 answers
55 views

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

2 votes
1 answer
116 views

Confusion about vanishing of ideal sheaves.

2 votes
0 answers
127 views

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

2 votes
0 answers
82 views

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

2 votes
1 answer
82 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?

2 votes
1 answer
155 views

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

2 votes
1 answer
102 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 $r$.