User Fred Akalin - Mathematics Stack Exchange

6 votes

0 answers

70 views

Showing that $\sum_{i = 1}^N \sum_{j = N - i + 1}^N \frac{1}{ij} = \sum_{i = 1}^N \frac{1}{i^2}$ without induction

asked Jul 1 at 1:56

5 votes

1 answer

201 views

Proving an evenness property for the nth power map for a finite (not necessarily commutative) group $G$

asked Jan 26, 2020 at 19:55

3 votes

1 answer

787 views

Can the Gram-Schmidt algorithm be extended to construct a basis for $T_p M$ of a semi-Riemannian manifold?

asked Jan 26, 2018 at 19:56

3 votes

1 answer

689 views

Does a coordinate chart have a smooth orthonormal frame w.r.t. a semi-Riemannian metric?

asked Jan 29, 2018 at 0:51

3 votes

0 answers

100 views

Reference request: The ring $k[x_1, \dotsc, x_n]/I$ as a limit of functions with distinct zeroes

asked Feb 3 at 22:49

2 votes

2 answers

223 views

How do I translate the intersection of two affine curves in a plane into a statement about ideals in $k[X, Y]$?

asked Nov 27, 2023 at 6:05

2 votes

1 answer

78 views

Do two lines passing through two (not necessarily distinct) points on an irred. cubic necessarily coincide? (Proof of Sec. 5.6, Prop. 3 in Fulton)

asked Jan 21 at 7:43

2 votes

1 answer

172 views

Localizing $\mathbb{Z}[X]/(2X, X^2)$ at $(2, X)$

asked Dec 14, 2018 at 5:44

2 votes

1 answer

63 views

If $f \colon M \to N$ is surjective, $K \subseteq \ker f \subseteq M$, and $M/K \cong N$, does that imply $K = \ker f$?

asked Dec 27, 2021 at 20:26

1 vote

0 answers

91 views

For naturality of the Lie bracket, doesn't the source functor have to take a manifold $M$ to $\mathfrak{X}(M) ⊗ \mathfrak{X}(M)$?

asked Jan 21, 2022 at 1:01

1 vote

1 answer

311 views

If $f ∈ C^∞(M)$ has vanishing first-order Taylor polynomial at $p$, is it a finite sum of $gh$ for $g, h ∈ C^∞(M)$ that vanish at $p$?

asked Jul 25, 2020 at 1:43

1 vote

2 answers

170 views

How do units work for objects in differential geometry?

asked May 27, 2017 at 8:16

1 vote

1 answer

320 views

What is the correct formula for the Ricci curvature of a warped manifold?

asked Jan 13, 2018 at 21:41

1 vote

1 answer

109 views

Do pp-wave spacetimes have a well-defined signature/index?

asked Jan 24, 2018 at 20:36

1 vote

0 answers

60 views

Does Fulton's proof of Cayley-Bacharach Theorem (two cubics that intersect a third cubic in 8 points share the 9th) require proof by contradiction?

asked Jan 22 at 23:15

0 votes

0 answers

78 views

Can the intersection multiplicity for plane curves be defined computationally?

asked Dec 7, 2023 at 8:22

0 votes

1 answer

143 views

Equivalence of definitions of simplicial manifolds, and which ones imply "no branching"

asked Feb 26, 2021 at 3:06

0 votes

0 answers

78 views

Under what conditions on $k$ is $V(X^2 - Y^3, Y^2 - Z^3)$ irreducible?

asked Nov 25, 2022 at 20:43

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18 Questions

Showing that $\sum_{i = 1}^N \sum_{j = N - i + 1}^N \frac{1}{ij} = \sum_{i = 1}^N \frac{1}{i^2}$ without induction

Proving an evenness property for the nth power map for a finite (not necessarily commutative) group $G$

Can the Gram-Schmidt algorithm be extended to construct a basis for $T_p M$ of a semi-Riemannian manifold?

Does a coordinate chart have a smooth orthonormal frame w.r.t. a semi-Riemannian metric?

Reference request: The ring $k[x_1, \dotsc, x_n]/I$ as a limit of functions with distinct zeroes

How do I translate the intersection of two affine curves in a plane into a statement about ideals in $k[X, Y]$?

Do two lines passing through two (not necessarily distinct) points on an irred. cubic necessarily coincide? (Proof of Sec. 5.6, Prop. 3 in Fulton)

Localizing $\mathbb{Z}[X]/(2X, X^2)$ at $(2, X)$

If $f \colon M \to N$ is surjective, $K \subseteq \ker f \subseteq M$, and $M/K \cong N$, does that imply $K = \ker f$?

For naturality of the Lie bracket, doesn't the source functor have to take a manifold $M$ to $\mathfrak{X}(M) ⊗ \mathfrak{X}(M)$?

If $f ∈ C^∞(M)$ has vanishing first-order Taylor polynomial at $p$, is it a finite sum of $gh$ for $g, h ∈ C^∞(M)$ that vanish at $p$?

How do units work for objects in differential geometry?

What is the correct formula for the Ricci curvature of a warped manifold?

Do pp-wave spacetimes have a well-defined signature/index?

Does Fulton's proof of Cayley-Bacharach Theorem (two cubics that intersect a third cubic in 8 points share the 9th) require proof by contradiction?

Can the intersection multiplicity for plane curves be defined computationally?

Equivalence of definitions of simplicial manifolds, and which ones imply "no branching"

Under what conditions on $k$ is $V(X^2 - Y^3, Y^2 - Z^3)$ irreducible?