Search Results
Search type | Search syntax |
---|---|
Tags | [tag] |
Exact | "words here" |
Author |
user:1234 user:me (yours) |
Score |
score:3 (3+) score:0 (none) |
Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
Views | views:250 |
Code | code:"if (foo != bar)" |
Sections |
title:apples body:"apples oranges" |
URL | url:"*.example.com" |
Saves | in:saves |
Status |
closed:yes duplicate:no migrated:no wiki:no |
Types |
is:question is:answer |
Exclude |
-[tag] -apples |
For more details on advanced search visit our help page |
Results tagged with ag.algebraic-geometry
Search options not deleted
user 13972
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
26
votes
Accepted
Algebraic surface of constant width?
There exist many algebraic surfaces of constant breadth with no continuous symmetries, even ones with no symmetries at all. To see this, consider the properties of the support parametrization:
The su …
13
votes
Accepted
A quadratic $O(N)$ invariant equation for 4-index tensors
Well, this is not actually an answer to either of the OP's questions; at most, it provides an easier way to classify the solutions for the $n=3$ case, and that might point a way towards an analysis fo …
8
votes
Are the quaternionic Grassmannians quaternionic Kaehler manifolds?
Perhaps the OP really wants to know why quaternionic Grassmannians other than the quaternionic projective spaces are not considered to be 'quaternion-Kähler'.
The reason goes back to Berger's classifi …
15
votes
Accepted
Algebraic atlas on smooth manifolds
The answers to your question in the case $n=1$ are well-known. In higher dimensions, the answers are less complete, but something is known.
For example, in the real case when $n=1$, there is only one …
53
votes
Accepted
When is a singular point of a variety ($\mathcal{C}^\infty$-) smooth?
NB: This answer is directed to the questions about the real case, not the complex case, which was already treated by Francesco. Added 5 July 2021: Because of some questions I have received over the …
5
votes
Invariant theory over $\mathbb R$
As YCor commented, the main point is to show that the invariant polynomials separate orbits. This follows from the compactness of $\mathrm{SO}(n)$. The point is this: Because $\mathrm{SO}(n)$ is co …
18
votes
Is every minimal hypersurface in $S^n$ algebraic?
The answer to this question is 'no' for most minimal surfaces of revolution in the $3$-sphere.
Consider surfaces in $S^3 = \{\,(z,w)\in\mathbb{C}^2\,|\,|z|^2+|w|^2=1\,\}$ that are invariant under the …
7
votes
Subspaces of $ A_{n}(\mathbb {Q})$ in which all nonzero matrices are invertible
For a field $\mathbb{F}$, let $\mu_\mathbb{F}(n)$ denote the maximal dimension of a subspace $N\subset A_n(\mathbb{F})$ such that all the nonzero elements of $N$ are invertible. For simplicity, I wil …
21
votes
Accepted
Problems concerning subspaces of $M_{n}(\mathbb{Q}) $
Let's call this maximal dimension function $\rho_{\mathbb{Q}}:\mathbb{N}\to\mathbb{N}$, i.e., $\rho_{\mathbb{Q}}(n)$ is the largest possible dimension of a subspace $N\subset M_n(\mathbb{Q})$ such tha …
4
votes
Accepted
Existence of complex function?
The answer is 'yes' there do exist such functions that are non-constant with singularities only along surfaces $\Sigma\subset\mathbb{C}^2$, and here is how one can understand them:
First, it helps to …
2
votes
Accepted
Product of subgroups of $SU(8)$ algebraic set?
Yes, $G_1G_2\subset\mathrm{SU}(8)$ is an algebraic set. Here is the argument:
Let $G_1{\times}G_2$ act on $\mathrm{SU}(8)\subset\mathrm{End}(\mathbb{C}^8)\simeq\mathbb{C}^{64}$ by the rule $(g_1,g_2) …
12
votes
Accepted
To describe an invariant trivector in dimension 8 geometrically
Here's another very nice (but still algebraic) interpretation that explains some of the geometry: Recall that $\operatorname{SL}(2,\mathbb{C})$ has a $2$-to-$1$ representation into $\operatorname{SL} …
1
vote
Accepted
Algebraic geometric conditions on the variety $V(F)$ such that the manifold defined by $F$ h...
As we know, the projective hypersurface in $\mathbb{P}^n$ defined by a homogeneous polynomial equation
$$
F(x^0,\ldots,x^n)=0
$$
of degree $m$ is nonsingular if $x=0$ is the only solution to the equat …
2
votes
Accepted
Question about the implicit function theorem. an example of a homogeneous form for which its...
Here is a simple example: Take $F = w^3 +3 w u^2 -v^3$ on $\mathbb{R}^3$ with coordinates $(u,v,w)$. At the point $p=(u,v,w)=(1,0,0)$, we have that $F=0$ can be solved for $w$ as a function of $(u,v …
14
votes
Unique almost complex structure up to diffeomorphism
Dmitri's answer is fine, but there is a different argument that is purely local that is worth bearing in mind as well:
On a $2n$-manifold $M$, the set of almost complex structures on $M$ are the secti …