The examples tag has no usage guidance.

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### Is there a smooth rationally connected, proper variety $M$ over $\mathbb{C}$ such that c_1(L)([A]) = 1 which is not projective space?

Is there a smooth, rationally connected, projective variety $M$, which is not a projective space and is equipped with an ample line bundle $L$, such that the homology class of the curves $[A]$ which ...

**0**

votes

**0**answers

182 views

### Examples of functions with natural boundary that do not satisfy Fabry or Hadamard gap theorem condition

there are examples of lacunary functions with natural boundary that do not satisfy Fabry or Hadamard gap theorem condition.I want to know more examples of those functions,the more the better,...

**4**

votes

**1**answer

319 views

### Example of a specific manifold

I want to find a example of a manifold that has positive scalar curvature but is not half conformally flat.
Does there exists such manifolds?
Thanks.

**1**

vote

**1**answer

201 views

### Examples of nontrivial local systems in Decomposition Theorem

There is a proper map $f: X \rightarrow Y$ of projective varieties. The Decomposition Theorem of Beilinson–Bernstein–Deligne-Gabber states that
$$Rf∗IC_X \cong \oplus_a IC_{\bar{Y_a}}(L_a)[shifts]$...

**3**

votes

**1**answer

163 views

### Mumford-Ramanujam examples in characteristic p [and in Arakelov geometry]

For a compact Riemann surface $B$ of genus $\geq 2$, it is a consequence of the Narasimhan-Seshadri theorem that there exist rank-$2$ vector bundles $E \to B$ of degree zero, all of whose symmetric ...

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votes

**2**answers

279 views

### How weird can Modular Tensor Categories be over non-algebraically closed fields?

I am trying to understand better the behaviour and character of modular tensor categories over non-algebraically closed fields. How weird can they be?
The reason I am interested in this is that my ...

**10**

votes

**3**answers

724 views

### Are all vector-space valued functors on sets free?

Let $\mathbf{Set}$ be the category of finite sets and functions between them, and let $\mathbf{Vect}$ be the category of finite-dimensional complex vector spaces and linear transformations between ...

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votes

**2**answers

421 views

### A sequence of subsets of an infinite group

Is there an infinite group $G$ such that there is not any sequence $(A_n)$ of its subsets such that always
$$A_n=A_n^{-1}, \quad A_{n+1}A_{n+1}\subsetneqq A_n$$
?
link

**5**

votes

**2**answers

208 views

### smooth affine surfaces over algebraically closed fields with trivial l-torsion of the Brauer group

I am looking for examples of smooth affine surfaces over algebraically closed fields with trivial $\ell$-torsion of the Brauer group.
Related questions: Schemes with trivial brauer group and Brauer ...

**2**

votes

**2**answers

260 views

### Example(s) of monoidal symmetric closed category with NNO without infinite coproducts?

The question is in the title, here is my motivation:
$\require{AMScd}$Let $(\mathcal C,\otimes,I)$ be a monoidal symmetric closed category. Then, the tensor product commutes with colimits, and if $\...

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votes

**0**answers

322 views

### Closed 4-manifolds with uncountably many differentiable structures

I know that $\mathbb{R}^4$ admits uncountably many differentiable structures and I was wandering what happen if we consider closed 4-manifolds. Are there any closed 4-manifolds with uncountably many ...

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votes

**0**answers

337 views

### Homeomorphisms of product spaces: an example

In the first of these lectures (http://www.mpim-bonn.mpg.de/node/4436) given by M. Freedman he says that there exists (compact metric) spaces $X$ and $Y$ such that $X\times S^{1}$ is homeomorphic to $...

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votes

**6**answers

470 views

### Do you have examples of such “transitive” elements?

(I've asked the same question at the MSE, so far with no answers, so I thought I'd try it here as well. If there's some clash with any site rules, please let me know and I'll abide.)
Let $A$ be a set ...

**4**

votes

**1**answer

216 views

### Unravelling some hypotheses on a variety

In Le group de Brauer II, Grothendieck states
Proposition 1.4.- Soit $X$ a préschéma noetherien. Supposon que les anneaux hensélisés stricts des anneaux locaux de $X$ soient factoriels, [...] ...

**82**

votes

**8**answers

9k views

### Mistakes in mathematics, false illusions about conjectures

Since long time ago I have been thinking in two problems that I have not been able to solve. It seems that one of them was recently solved. I have been thinking a lot about the motivation and its ...

**4**

votes

**3**answers

152 views

### A model with $\kappa$ many automorphism and a rigid element.

The following should be known, but I could not find an example.
Let $\kappa$ be an uncountable cardinal. Find a model $M$ of size $\kappa$ which has $\ge\kappa$ many automorphisms, but for some $m\in ...

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votes

**1**answer

127 views

### Simple but topologizable [closed]

Do you have an example of an infinite simple group with at least 3 distinct group topologies on it?

**0**

votes

**1**answer

228 views

### Examples of groups such that order isomorphism of the subgroups of $G\times G$ and $H\times H$ does not imply isomorphism of $G$ and $H$

Let $G$ and $H$ be groups, $\operatorname{Sub}(G\times G)$ be the set of all subgroups of $G\times G$ and $\operatorname{Sub}(H\times H)$ be the set of all subgroups of $H\times H$. Assume there ...

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votes

**1**answer

223 views

### Measures which exhibit the “uncorrelated implies independent” property

Let $X$ be a topological linear space, and let $X^*$ be its dual space. Suppose that $X$ is complete and Hausdorff, and $X^*$ separates points. Let $Y$ be another such space, and let $f : X \to Y$ be ...

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vote

**0**answers

133 views

### Examples of languages that are in P and are not in CFL [closed]

Any examples of languages that are in P(polynomial time to recognize it) and are not in CFL(context-free language)?The more the better.

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votes

**1**answer

254 views

### Nontrivial upper bounds on proof-theoretic ordinals of strong theories: do we have any?

Motivated by Consistency of Analysis (second order arithmetic) and Proof-Theoretic Ordinal of ZFC or Consistent ZFC Extensions?, I have the following question:
Are there any examples of strong ...

**3**

votes

**3**answers

819 views

### Fibrations with isomorphic fibers, but not Zariski locally trivial

(I posted this same question on MSE. Sorry if it is too elementary.)
I am looking for examples of fibrations $f:X\to Y$ where the fibers are all isomorphic, but $f$ is not Zariski locally trivial. In ...

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votes

**1**answer

314 views

### Not quite adjoint functors

What are standard and/or natural examples of pairs of functors $F:C\leftrightarrows D:G$ and unnatural bijections $\hom_D(Fx,y)\to\hom_C(x,Gy)$ for all $x$ and $y$? Can one do this so that the ...

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votes

**1**answer

247 views

### Semitransitive relations

By a digraph, let us mean an ordered pair $(X,r)$ with $r : X \times X \rightarrow B,$ where $X$ is a set and $B = \{\mathrm{False}, \mathrm{True}\}.$
Then supposing $\mathbb{X} =(X,r)$ is a digraph, ...

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votes

**1**answer

481 views

### Examples of “nice” properties of algebraic extensions of $\mathbb{Q}$

I am writing a short survey of some "nice'' properties of algebraic extensions of $\mathbb{Q}$. Let's say a property (P) is nice if
every finite extension of $\mathbb{Q}$ satisfies (P), and
if $K ...

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votes

**9**answers

2k views

### What are your favorite concrete examples of limits or colimits that you would compute during lunch?

(The title was initially "What are your favorite concrete examples that you would compute on the table during lunch to convince a working mathematician that the notions of limits and colimits are not ...

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votes

**5**answers

1k views

### Examples of ubiquitous objects that are hard to find?

I've been wrestling with a certain research problem for a few years now, and I wonder if it's an instance of a more general problem with other important instances. I'll first describe a general ...

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votes

**7**answers

787 views

### Examples of toposes for analysts

I've read that toposes are extremely important in modern mathematics, but I find the definitions and examples given on the nLab page a little too abstract to understand.
Can you provide some examples ...

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votes

**1**answer

205 views

### Vanishing Cech cohomology

Let $X$ be a manifold such that $dim(X)=n$. It is well-know that if $\mathcal{F}$ is a coherent sheaf $H^m(X,\mathcal{F})=0$ for all $m >n$ (where I denote with $H(-)$ Cech cohomology). But is ...

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votes

**3**answers

569 views

### A non-trivial probability measure on $2^{\mathbb R}$

Consider the measurable space $2^{\mathbb R}$, equipped with the tensor-product $\sigma$-algebra. Famously, this space has a measurable structure which is not generated by a topology (see this answer)....

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vote

**1**answer

327 views

### Examples of Quot schemes

I'm studying Quot schemes, that I denote with $Quot_{N,X,P}$, with $N \in \mathbb{Z}$, $X \subset \mathbb{P}^d$ and $P \in \mathbb{Q}[t]$. So, I'm looking for explicit examples of Quot schemes. Could ...

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votes

**5**answers

1k views

### are there natural examples of classical mechanics that happens on a symplectic manifold that isn't a cotangent bundle?

I'm curious about just how far the abstraction to a symplectic formalism can be justified by appeal to actual physical examples. There's good motivation, for example, for working over an arbitrary ...

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votes

**2**answers

228 views

### Natural $\Pi^1_2$ (or worse) classes of structures?

(To clarify, my interest is mainly lightface, that is, $\Pi^1_2$ instead of $\bf \Pi^1_2$, although it doesn't particularly matter.)
This is just an idle curiosity. In logic, I find myself frequently ...

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votes

**1**answer

994 views

### Learning a little Motivic Cohomology

Simply because I find it interesting, I have spent some time studying motivic cohomology from the lectures by Mazza, Voevodsky and Weibel. However, I'm finding it hard to tell if the theory is ...

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vote

**1**answer

90 views

### Existence of a moderate uniform structure on $\Bbb R$

A moderate uniform structure $\mathcal U$ on $\Bbb R$ is one for which
$\forall U\in \mathcal U, \exists n\in \Bbb N,\quad U^n=\Bbb R^2$
but
$ \not\exists n\in \Bbb N,\forall U\in \mathcal U,\quad U^...

**4**

votes

**1**answer

423 views

### Uncountable Reduced ring $R$ with $R[x]$ has only a countable number of maximal left ideals

The question is following:
Is there an uncountable reduced ring (i.e., a ring with no non-zero nilpotent element) $R$ (with identity) such that
$R[x]$ has only a countable number of maximal ...

**12**

votes

**2**answers

585 views

### Occurrences of D. H. Lehmer's 10-th degree polynomial

Salem numbers and Lehmer's minimum height problem are venerated not only in number theory and diophantine analysis, where they are considered naturally interesting for their own sake, but also in ...

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**13**answers

2k views

### An example of a proof that is explanatory but not beautiful? (or vice versa)

This question has a philosophical bent, but hopefully it will evoke straightforward, mathematical answers that would be appropriate for this list (like my earlier question about beautiful proofs ...

**6**

votes

**1**answer

343 views

### Generating functions with all non-zero coefficients equal to one

Inspired by this question, I have been wondering if there are any useful generating functions with all non-zero coefficients equal to one. Obviously, the trivial generating function $\frac{1}{1-x}$ ...

**23**

votes

**1**answer

1k views

### Example of 4-manifold with $\pi_1=\mathbb Q$

This might be well known for algebraic topologist. So I am looking for an explicit example of a 4 dimensional manifold with fundamental group isomorphic to the rationals $\mathbb Q$.

**1**

vote

**0**answers

432 views

### Homotopy theory of schemes

I have seen the notion of Homotopy come up in several contexts in schemes. For example, the book "Lectures on Motivic Cohomology" by Mazza, Weibel and Voevodsky uses this language to some extent. I.e. ...

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votes

**4**answers

421 views

### Order-independent properties arising naturally in mathematics

The motivation for the following question comes from finite model theory,
but it is not a technical question about this field,
and it is particularly directed at people working in other fields.
It ...

**4**

votes

**1**answer

165 views

### A group 3-cocycle, trivial on a pair of generating subgroups?

I'm looking for an example of the following situation:
A group $G$ generated by finite subgroups $H$ and $K$,
a non-trivial 3-cocycle $\omega \in H^3(G, \mathbb{k}^\times)$
such that
the ...

**13**

votes

**1**answer

620 views

### Examples of polynomial rings $A[x]$ with relatively large Krull dimension

If $A$ is a commutative ring we have the estimate
$$
\dim (A)+1 \le \dim (A[x])\le 2\dim (A)+1
$$
for the Krull dimension, with $\dim (A)+1 = \dim (A[x])$ for Noetherian rings.
I am looking for nice ...

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votes

**1**answer

255 views

### Satellite knot example

Can someone provide me with an example of a satellite knot with symmetry group which is neither cyclic nor dihedral?

**8**

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**7**answers

1k views

### Gelfand representation and functional calculus applications beyond Functional Analysis

I think it is fair to say that the fields of Operator Algebras, Operator Theory, and Banach Algebras rely on Gelfand representation and functional calculus in a crucial way.
I am curious about ...

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votes

**1**answer

222 views

### Methods to tell if a magma has idempotents

(Disclaimer: below, when I say "compact" I mean "compact Hausdorff.")
I asked a version of this question on math stackexchange (http://math.stackexchange.com/questions/305186/left-continuous-magmas-...

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votes

**2**answers

317 views

### What is a good example of a hyperspace where the base space is non-Hausdorff?

Let $X$ be a topological space, and let $\operatorname{CL}(X)$ be its hyperspace. That is, $\operatorname{CL}(X)$ is the set of closed subsets of $X$, equipped with the minimal topology so that the ...

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**2**answers

1k views

### Good examples of random variables whose image is not a measurable set?

Are their simple/natural examples of real-valued Borel-measurable random variables whose image is not a Borel set? Something that occurs "naturally"?
I am teaching Doob's lemma (for two real-valued ...

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**1**answer

2k views

### Example of fiber bundle that is not a fibration

It is well-known that a fiber bundle under some mild hypothesis is a fibration, but I don't know any examples of fiber bundles which aren't (Hurewicz) fibrations (they should be weird examples, I ...