# All Questions

**6**

votes

**1**answer

218 views

### Singularities of the moduli stack of Calabi-Yau threefolds

Let $M$ be the moduli of polarized Calabi-Yau threefolds over $\mathbb C$ with fixed Euler characteristic. The coarse moduli space is singular (as usual), but what about the stack?
In many cases I ...

**0**

votes

**0**answers

61 views

### $\inf\{i\in \mathbb N \cup \{0\}\cup\infty\mid Ext^i_R(R/I,R)\neq 0\}=0 ?$

Let $R := k[x_1, \cdots, x_n, \cdots]/(x_1^1, \cdots , x^n_n, \cdots),$ where $k$ is a field. Set $I:=(x_1, \cdots, x_n, \cdots)$. the questions are:
Is $\inf\{i\in \mathbb N \cup \{0\}\cup ...

**0**

votes

**0**answers

28 views

### Reflexive sheaves on stable curves-II [migrated]

This is an extension of Reflexive sheaves on stable curves.
Let $C$ be a stable curve and $\mathcal{F}$ a reflexive sheaf on $C$ supported on the whole of $C$. Is the projective dimension of ...

**5**

votes

**0**answers

137 views

### Size of smallest multiple $\sum \epsilon_i p^i$ of $n$ with digits $\epsilon_i\in \{0,1\}$ for $p$ a prime

Any natural number $n$ coprime with a prime number $p$ is a divisor of
$M=1+p+p^2+\dots+P^{N-1}$ where $N\leq \varphi((p-1)n)$ is the order of
$p$ in $\left(\mathbb Z/((p-1)n)\mathbb Z\right)^*$.
...

**7**

votes

**0**answers

92 views

### Some $q-$analogues of $ \sum\limits_{j = - k}^k {{{( - 1)}^{ j}}}\binom{n}{k-j}\binom{n}{k+j}=\binom{n}{k}.$

Let ${\left( {a;q} \right)_n}=\prod\limits_{j = 0}^{n - 1} {(1-{q^j}a} )$ and
let $ {{n}\brack{k}}_q$ denote a $q-$binomial coefficient.
I am interested in $q-$analogues of the identity $ ...

**1**

vote

**0**answers

22 views

### Eigenvalue overdetermined problem

Consider the following overdetermined eigenvalue problem for $\Omega \subset \Bbb{R}^2$:
$$(1) \ \ \ \ \begin{cases} - \Delta u = \lambda u & \text{ in }\Omega \\
u = 0 ...

**0**

votes

**0**answers

58 views

### Reflexive sheaf on normal surfaces [migrated]

Let $X$ be a normal, projective scheme of pure dimension $2$ and $\mathcal{F}$ is a reflexive coherent sheaf on $X$. Is $\mathcal{F}$ locally free?

**1**

vote

**1**answer

52 views

### Strict comma objects implies comma objects

I'm condusion on a statement in this page comma object in $n$lab. It states:
any strict comma object is a comma object, but the converse is not in general true.
My confusion is: the strict comma ...

**0**

votes

**0**answers

30 views

### How to compute the best fitting frustum for a set of points? [on hold]

My first post on MathOverflow !
I am struggling with a problem that I am sure is well known, but I could not find any answer using google or searching on MathOverflow.
I have a set of 3D points ...

**3**

votes

**0**answers

133 views

### name for an intermediate notion between huge and 2-huge

I am employing a large cardinal notion that has been used explicitly before, and I am wondering if someone has given it a good succinct name.
A cardinal $\kappa$ is huge if there is an elementary $j ...

**7**

votes

**2**answers

160 views

### p-adic analogue of the Strong Law of Large Numbers

Is there a $p$-adic analogue of the Strong Law of Large Numbers? In particular, suppose that $f_i: \mathbb{Z}_p \longrightarrow \mathbb{Q}_p$ for $i = 1,2,\ldots$ is an sequence of random variables ...

**-2**

votes

**0**answers

114 views

### Can a numerical system be built following these ideas? (decomposition of infinity) [on hold]

I have been some time thinking on how to reconcile non-Archimedean extentions of real line with results on summation of divergent series.
Now suppose $\Omega$ is an infinite quantity, the number of ...

**-2**

votes

**0**answers

16 views

### How do i find the maximum area for a crate, that has to fit inside a shape? [on hold]

Here's the shape: http://i.stack.imgur.com/WrY7V.png
h is equal to: 3.57meters and d is equal to 5.28 meters, I've tried to setup a formula for the area, but i cant seem to get a valid one. Any help ...

**1**

vote

**0**answers

27 views

### Is the order convergence topology on a poset always Hausdorff?

In this post two topologies on a poset $(P,\leq)$ were defined: the interval topology $\tau_i(P)$ and the order convergence topology $\tau_o(P)$. It turns out that $\tau_i(P)$ is always $T_1$ and ...

**4**

votes

**1**answer

57 views

### Does every locally compact Hausdorff space admit a locally finite open covering by relatively compact sets?

Let $X$ be a locally compact Hausdorff space. Does there exist a locally finite open covering consisting of relatively compact sets?

**10**

votes

**1**answer

339 views

### Class field towers

It is known (Golod and Shafarevich) that the class field tower of a finite extension $K$ of $\mathbb{Q}$ may be infinite. But is it always finite for $K=\mathbb{Q}[\zeta]$ where $\zeta$ is a root of ...

**0**

votes

**3**answers

95 views

### Extension of conformal map and annulus

My question is the following : suppose you have a doubly-connected open set $\Omega \subset \mathbb{C}$, that is a domain bounded by 2 non-intersecting circles $C_1$ (the interior) and $C_2$ (the ...

**1**

vote

**1**answer

43 views

### ideals of polynomial ring of two variables generated by two elements

Let $f,g$ be two polynomials in $\mathbb{Z}[x,y]$, given by
$$
f(x,y)=x^4-3xy+y^2,$$
$$
g(x,y)=x^5-4xy+3xy^2.$$
Let $I=(f,g)$ be the ideal in $\mathbb{Z}[x,y]$ generated by $f$ and $g$.
Is ...

**-1**

votes

**0**answers

76 views

### X^2 + 4 = y^5 is there any solution to this [on hold]

is there any integer solution to the given equation?
i have tried to solve the problem considering modulo of different prime but it just aint working
it'd be nice if i get a solution soon

**1**

vote

**0**answers

69 views

### Does Kaplansky's Zero Divisor Conjecture hold valid for (torsion-free) residually finite groups?

Kaplansky's Zero Divisor Conjecture states that the group algebra $KG$ has no zero divisor for any field $K$ and any torsion-free group $G$.
Does Kaplansky's Zero Divisor Conjecture hold valid ...

**2**

votes

**1**answer

75 views

### Stochastic differential equation associated with an optimal control problem

We know how to find the stochastic differential equation (Hamilton-Jacobi-Bellman equation, HJB) of the control problem where a process $X_t$ is controlled up until it is stopped at a stopping time ...

**6**

votes

**0**answers

212 views

### Reference for “if the set $A$ is Suslin, then every $\Sigma^1_1(A)$ set is Suslin”

Does anyone know of a reference for one or both of the following facts (in $\mathsf{ZF}$)?
If the set of reals $A$ is Suslin, then every $\Sigma^1_1(A)$ set of reals is Suslin.
If $T$ is a tree on ...

**2**

votes

**0**answers

36 views

### Generation of compact Lagrangians over fields with characteristic 2

Let $\pi:X\rightarrow\mathbb{C}$ be a Lefschetz fibration, and assume that the fibers are exact or monotone. A classical result of Seidel says that all the closed weakly unobstructed Lagrangian ...

**0**

votes

**0**answers

56 views

### induced map on tangent bundles from blow up morphism

Suppose $X$ is the plane nodal curve over $\mathbb{C}$. Then we can mimic what we do in differential geometry to define the "tangent bundle" over $X$ as a subvariety of ...

**-1**

votes

**0**answers

137 views

### Limit Group decomposition

I would need a clarification about a statement in the article Limit groups and groups acting freely on $\mathbb{R}^n$-trees by Vincent Guirardel.
First recall that a limit group is a finitely ...

**0**

votes

**0**answers

52 views

### Gaussian Measure for Random Matrix [on hold]

I am doing physics and do not have enough mathematical background. so the question may be trivial, I apologize for that. any help and suggestion for readable papers/books would be highly appreciated. ...

**1**

vote

**1**answer

68 views

### Balls from bin with replacement, distinct elements, concentration inequality

Draw $n$ numbers, denoted by $a_1, a_2, \ldots, a_n$, from set $[n]$, that is, for each $i$, $a_i$ is a uniformly random number from $[n]$.
Let $A = \{a_1, a_2, \ldots, a_n\}$. Then
$$
...

**0**

votes

**0**answers

71 views

### Unbounded polynomials [migrated]

Let $p(x)$ be a polynomial of degree $d$ on $R^n$, and let $\tilde{p}(x)$ be the homogeneous components with degree $d$, then how do we prove that:
if $\tilde{p}(x)$ is unbounded below, then $p(x)$ ...

**-2**

votes

**2**answers

134 views

### On Bohr-MollerupTheorem [on hold]

In http://mathworld.wolfram.com/Bohr-MollerupTheorem.html, Bohr-Mollerup Theorem is given where it is stated that $\Gamma$ function is the unique log convex function that satisfies ...

**1**

vote

**0**answers

133 views

### Monoidal Forgetful/Free Adjunction for $E_2$-algebras

Suppose I am given two $E_2$-ring spectra $A$ and $B$ and a morphism of $E_2$-rings $\phi:A\to B$. Then I have $E_1$-monoidal categories of modules $LMod_A$ and $LMod_B$. Moreover I have morphisms ...

**1**

vote

**2**answers

188 views

### A question involving Mazur's Lemma

Consider the Mazur's Lemma (H. Brezis - "Functional analysis, ..."):
"Assume $(x_n)$ converges weakly to $x$. Then there exists a sequence $(y_n)$ made up of convex combinations of the $x_n$'s that ...

**0**

votes

**1**answer

121 views

### Reflexive sheaves on stable curves

Let $C$ be a stable curve over an algebraically closed field of positive characteristic and $\mathcal{F}$ be a reflexive sheaf on $C$. Is $\mathcal{F}$ locally free?
EDIT Is the projective dimension ...

**7**

votes

**1**answer

177 views

### Asymptotic limit of truncated Legendre sieve

Consider the truncated sum
$$
S(x):=\sum_{\substack{{d\mid P(\sqrt{x})}\\{d\leq x}}}\mu(d)/d,
$$
where $P(z)$ is the product of all primes less than or equal to $z$, and $\mu(d)$ is the Möbius ...

**2**

votes

**1**answer

203 views

### Can states on commutative Banach algebras be understood as probability measures?

Suppose $\mathcal{A}$ is a commutative Banach algebra. Is there always a measurable space $(\Omega,\mathcal{F})$ such that there is a bijective correspondence between states on $\mathcal{A}$ and ...

**0**

votes

**1**answer

96 views

### Base change of regular schemes [on hold]

Let $R$ be a complete DVR with fraction field $K$, $X$ be a regular scheme flat over $R$. Let $L$ be a finite field extension of $K$ and $Q$ be the integral closure of $R$ in $L$. Denote by $Y:=X ...

**1**

vote

**1**answer

103 views

### compact inclusion of domains of unbounded operators

Let $L$ be a positive self-adjoint operator defined densely on $L^2(M)$ where $M$ is a compact manifold.
Also, let $\mathcal{D}(L) \subset H^1(M)$. It is known that $\mathcal{D}(L) \subset ...

**3**

votes

**0**answers

53 views

### Pointwise (a.e) evaluation of $\sum_{n \geq 0}(u,w_n)_{L^2}w_n$ and equalities in $L^2$

Let $w_n$ be a orthonormal basis of $L^2(\Omega)$. Given $u \in L^2$ we can write $$u=\sum_{n \geq 0}(u,w_n)_{L^2}w_n.$$
Suppose $w_n$ are the eigenfunctions of the Neumann Laplacian. We can write
...

**2**

votes

**1**answer

126 views

### How to show that there's a continuous function separating convex sets of Radon measures?

First, the setup: $X$ is a compact set. By Riesz's representation theorem $C(X)^*=${all Radon measures on $X$}. $K$ is a convex, closed set of probability measures. $m$ is a probability measure out of ...

**9**

votes

**1**answer

166 views

### Is the analytic version of the Whitney Approximation Theorem true?

I initially asked this question on MSE but I haven't had any luck.
The Whitney Approximation Theorem states that any continuous map between smooth manifolds is homotopic to a smooth map. If the ...

**-3**

votes

**0**answers

29 views

### Conditional probabilities [on hold]

Does it make sense to say :
$$\mathbb{P}\left(A|C\cap B|C\right)=\mathbb{P}\left(\left(A\cap B\right)|C\right)$$
And have we an associativity :
...

**3**

votes

**3**answers

187 views

### A question on flasque sheaf

Let $0\to \mathscr{F}'\to\mathscr{F}\to\mathscr{F}''\to 0$ be an exact sequene of sheaves. It is well known that $\mathscr{F}$ flasque iff $\mathscr{F}''$ flasque provided $\mathscr{F}'$ is flasque. ...

**-1**

votes

**0**answers

80 views

### Is there a version of decomposition theorem for smooth open manifolds in dimensions grater than 3? [on hold]

Is there a version of decomposition theorem http://www.jstor.org/stable/2034963
for smooth open manifolds in dimensions grater than 3?
There is two things about the cited theorem: it is for ...

**3**

votes

**0**answers

52 views

### Trapped Billiard trajectories on non-convex billiard tables

Let $\Omega$ be a domain in $\mathbb{R}^2$ with smooth boundary. A billiard trajectory is a continuous curve $c: \mathbb{R}\supseteq I \longrightarrow \overline{\Omega}$ such that
$c(t) \in ...

**-3**

votes

**0**answers

43 views

### What is a constant-rank matrix definition? [on hold]

I have had no luck finding a definition of constant-rank matrix. Even less luck with an intuitive example.
My interest is to understand when can I apply a formula for the derivative of the ...

**-4**

votes

**0**answers

33 views

### If Linear equations solution is inconsistent? [on hold]

Hello,
If my Linear equation system's martix is inconsistent.
There is no point to check homogenus system's solution, and I can safely say that the asked system has no solutions. Or am I wrong?

**1**

vote

**0**answers

77 views

### When can the rank of a submodule be bigger than the rank of the module itself? [migrated]

It is well known that the dimension of a subspace is less than or equal to the dimension of the vector space it is contained in. The same is true e.g. for modules over a principal ring.
I am looking ...

**1**

vote

**0**answers

30 views

### References to study Weak and Strong Topologies and aproximations on function spaces of manifolds

I´m studing weak and strong topologies and aproximations on the function space $C^{\infty}(M,N)$ of two manifolds $M$ and $N$. I´m using the book Differential Topology of Morris Hirsch but it is a ...

**-4**

votes

**0**answers

61 views

### Graph theory and topology [on hold]

I have related topological ideals with vertex magic totallabeling in graph theory. Is there any possibility to relate vertex magic totallabeling with generalized topology in a very interesting way? ...

**11**

votes

**2**answers

795 views

### When does Vopěnka's principle hold?

Vopěnka's principle (VP) is the statement that, given any proper class $\{\mathcal{A}_\eta: \eta\in ON\}$ of first-order structures in the same language, there are some $\alpha\not=\beta$ with ...

**2**

votes

**1**answer

404 views

### learning Deligne-Lusztig theory

Can someone give me a roadmap for learning Deligne-Lusztig theory? (Except for the original article by Deligne and Lusztig)
Edit: You may assume knowledge of representation theory of finite groups ...