All Questions
5,074 questions with no upvoted or accepted answers
1
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210
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Prime Fano manifolds of coindex 4 or 5.
Let $X\subset\mathbb{P}^N$ be a non-degenerate smooth complex projective variety (manifold for short).
Recall that $X$ is called prime Fano if $Pic(X)=\mathbb{Z}\langle \mathcal{O}(1)\rangle$ and if ...
- 1,159
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0
answers
318
views
Where can I find an English translation of Grauert's paper?
The german title is : Holomorphe Funktionen mit Werten in komplexen Lieschen Gruppen.
- 778
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0
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119
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Embeddings of spherical Kac-Moody varieties?
There is a well established theory of embeddings $G/H \to X$ into a normal variety $X$ where $G$ is a reductive group over an algebraically closed field and the image of any Borel $B$ is open in $X$; ...
- 3,968
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282
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Complexity of a problem related to 3D matching?
Given a set of triples of a base set $S$, find a subset of triples such that each element in $S$ appears exactly in one triple. This problem is NP-complete by reduction from NP-complete problem 3D ...
- 2,993
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0
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171
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Explicit construction of irreducible unitary connections
On a Riemann surface irreducible unitary connections on complex vector bundles of rank $n\geq 2$ are uniquley determined by their underlying holomorphic structure $\frac{1}{2}(\nabla+i*\nabla)$, where ...
- 6,825
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389
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Has anyone seen this version of ring toss (combinatorial object) before?
In reference to a
question on work of Westzynthius and another
question relating to Jacobsthal's function, I have formed a game which I immodestly call Paseman's Ring Toss. I hope that it has been ...
- 13k
1
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0
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279
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Linear differential equations with regular singularities
Consider a differential equation
$$
\delta^n+b_1(z)\delta^{n-1}+\ldots+b_n(z)
$$
with a regular singular point zero. (Here $\delta=z\frac\partial{\partial z}$). Assume that its indicial polynomial $\...
- 1,590
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765
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Which statement do people usually call the Decomposition Theorem, and what is the precise reference for it?
Which statement is usually called the Decomposition Theorem (for perverse sheaves)? Is this (roughly): a proper pushforward of an intersection complex could be decomposed into a direct sum of (shifted)...
- 16.9k
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187
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Watson Transformation Squared reference request
See
http://www.numbertheory.org/obituaries/OTHERS/watson.html
George Leo Watson (1909-1988) wrote in a conversational manner, it is difficult to see when he switches from the trivial to the ...
- 25.7k
1
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110
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Reference for existence of the trace on $R\rtimes_{\sigma_\phi}{\mathbb R} $ for $\phi$ being f.s.n. weight.
I am looking for a good reference for existence of the trace on $R\rtimes_{\sigma_\phi}{\mathbb R} $ for $\phi$ being f.s.n. weight.
For the $\phi$ being f. strictly s.n. weight it is probably van ...
- 21
1
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0
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137
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Number of ways to separate a terminal from labelled vertices in a graph
I have a question about the number of different ways to separate a terminal vertex from labeled vertex sets in a simple graph. There is a bound on this number that I am interested in. I have succeeded ...
- 495
1
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0
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436
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topological B model
The topological A model was constructed by Witten in Comm. Math. Phys. Volume 118, Number 3 (1988), 411-449. I am looking for the original paper where topological B model was first introduced. I am ...
- 3,218
1
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0
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396
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Notation for bilinear form $y^t M z$, where $M$ is a matrix and $y,z$ are vectors.
I'm working on a problem where I need to consider a bilinear form of the form $y^t M z$ where $M$ is an $n$-by-$n$ real symmetric matrix and $y,z \in \mathbb{R}^n$ are vectors. I also need to consider ...
- 4,922
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260
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Looking for paper "The cyclotomic identity" by Metropolis and Rota
I am looking for a copy of the paper in the title, appeared in the proceedings
"Combinatorics and algebra (Boulder 1983), Contemp. Math., 34"
and reprinted in
"Gian-Carlo Rota on Combinatorics, ...
- 4,492
1
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answers
270
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References for shimura curve moduli of abelian varieties of dimension 3?
I have not much background of it ,so I want to konw is there any pepers study family of abelian threefolds parametric by shimura curve?
- 709
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182
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G-Modules on X=G/H modules on X/H ?
I think it is true that $G$-equivariant sheaves on $X$ are equal to $G/H$ equivariant sheaves on $X/H$. More precisely I'm interested in the following statement:
Given an algebraic group $G$ with ...
- 13.2k
1
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268
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Learning statistical mechanics for non-particle phenomena
I'm interested in various areas of complex systems, and I often come across articles like these:
http://arxiv.org/PS_cache/cond-mat/pdf/0106/0106096v1.pdf
http://arxiv.org/abs/cond-mat/9804180
The ...
- 2,383
1
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2
answers
2k
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Bounding the norm of the Laplacian of the gradient of a function having Lipschitz continuous Hessian
It seems that the following claim is true, but I did not manage to prove it neither to find a reference.
Claim Let $f:\mathbb R^p\to\mathbb R$ be a three times differentiable function such that its ...
- 11
1
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1
answer
464
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Formulas for $\arg\max$
are any formulas for $\arg\max(f(x))$ known
(in the context of this question, $\max(f(x))$ shall denote the essential supremum of $f(x)$ over some given domain $\Omega\subset X$)?
The reason for ...
- 13.2k
1
vote
1
answer
603
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Is there any current development of a first order formalization of metamathematics?
I hope that this post isn't off topic, but I already asked math.stackexchange about first order formalizations of first order logic. There are provability logics and extensions in modal logic's that ...
- 223
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0
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20
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Unitaries that setwise fix an algebra under conjugation
Let $M_d(\mathbb{C})$ denote the algebra of $d \times d$ complex matrices. Consider the algebra
$$\mathcal{A} = \bigoplus_{i=1}^r I_{d_i} \otimes M_{d_i}(\mathbb{C})$$
for some choice of $d_1, \ldots, ...
- 2,339
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25
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Can I get a long exact homology sequence from a short exact sequence of graded commutative differential algebras over a field?
The category of differential graded commutative algebras over a field of characteristic 2 seems to have some not so nice properties. I could not find an answer in StackExchange as to why this category ...
- 35
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36
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Request for resources on directional derivative of the Riemannian distance function, and Berger's lemma about geodesics realizing the diameter
I've been recently interested in directional derivatives of the Riemannian distance function, and I came across this question, and its answer by Sergei Ivanov, where he stated an important result: (I ...
- 1,467
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31
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Looking for a citation for this simple generalization of the Markov bound to non-negative super-martingales
Does anybody know a reference for the following theorem?
Theorem 1. Let $(X_t)_{t=0}^\infty$ be a non-negative supermartingale.
Then, for any constant $c > 0$, the event $(\exists
> t)\, X_t \...
- 183
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0
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43
views
Equivalent conditions for $z$-embeddability
I am looking for where this specific theorem of Blair is originally located:
Theorem. Let $S\subseteq X$, the following are equivalent:
$S$ is $z$-embedded
If $A, B\subseteq S$ are disjoint zero-...
- 1,211
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0
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81
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Reference for computing cohomology of $Q_nS^0$ (the $n$-th component of infinite loop space)?
$Q_nS^0=\varinjlim_k(\Omega^kS^k)_n$, where $(\Omega^kS^k)_n$ refers to homotopy classes of maps $(S^k,\ast)\to (S^k,\ast)$ of degree $n$. I already know the case of $n=0$.
Is there any reference ...
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22
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Has this notion of "variation along the diagonal of a not-necessarily-smooth function" been studied before?
I am interested in knowing whether something along the lines of the "diagonal variation" defined below has been studied before. In spirit, the basic idea is that it is a kind of ...
- 708
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answers
190
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About Chern classes via Atiyah class
I am trying to understand a construction of the Chern classes of a vector bundle $\mathcal{E}$ via the Atiyah class, like is done in this text and here in section 1.4. I am interested in the case ...
- 348
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141
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State of the art on attempts to solve the elliptic curve discrete logarithm problem through transfering the problem to a weaker curve
Let an elliptic curve $E$, and 2 points on such curve $P$ and $O$ the methods I’m talking about consist in creating a weaker elliptic curve $F$ and mapping $P$ and $O$ to $F$ while successfully ...
- 87
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61
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Defining rank of an abelian subgroup using the second centralizer
I recently posted this on MSE, but didn't receive any feedback; so I'm posting it on MO.
I recently came across this article which explored the maximal abelian subgroups of the symmetric group $S_n$. ...
- 195
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55
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reference request: conditions for pointwise and operator-norm convergence of kernel projections
At a very high level, I’m interested in the following question. Suppose $X$ is a (separable) Hilbert space, and $T_n : X \rightarrow X$ is a sequence of finite rank self-adjoint maps that converges (...
- 101
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42
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Reference request: in Alexandrov geometry gradient flows preserve extremal subsets
It is mentioned in literature that in Alexandrov geometry gradient flows of semi-concave functions preserve each extremal subset.
I am looking for a proof of this fact.
- 21.8k
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52
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Reference request for the determinant of a matrix constructed from Pascal's triangle
One can prove by induction that the matrix $M^{(n)}$ given by
$$ \begin{pmatrix}
1 & 1 & 1 & 1 & \dots & \binom{n}{0} \\
1 & 2 & 3 & 4 & \dots & \binom{n+1}{1} \...
- 5,546
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0
answers
80
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Relation between Chow groups and K theory
I am reading about Chow groups and algebraic K-theory of schemes. I get to know that for smooth schemes the re is a strongly convergent spectral sequence
$$E_2^{p,q} = CH^{-q}(X,-p-q) \implies K_{-p-q}...
- 629
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106
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Generalizing the property of linear independent set in infinite dimensional TVS
Given a infinite dimensional Hilbert space $H$, and a countable set of vectors $\{v_{i}\}_{i=1}^{\infty}$. I want to study the following property of $\{v_{i}\}_{i=1}^{\infty}$:
There exists sequences $...
- 523
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0
answers
33
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Non-positive definite solution for differential Riccati equation
Consider the matrix-valued differential Riccati equation (DRE):
$$
\dot P_t +PA+A^\top P+Q-(B^\top P+S)^\top (B^\top P+S)=0, \quad t\in [0,T];\quad P(T)=G,
$$
where all coefficients are continuous.
...
- 503
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votes
0
answers
79
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Definition of Moore-Penrose inverse for unbounded self-adjoint operators?
I know there is a concept of Moore-Penrose or pseudoinverse of a matrix. I would like to know if one can define it for densely defined unbounded self-adjoint operators on Hilbert spaces as well. ...
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101
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Identities for Prime Coefficients of Certain Cusp Forms
While working with Fourier expansions of cusp forms of congruence subgroups of the modular group, I observed the following patterns in their prime coefficients.
Let $a(n)$ be the Fourier coefficients ...
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69
views
Projection of a gaussian random vector onto a convex body
Let $K \subset \mathbb{R}^n$ denote a convex body. Let $\Pi_K$ denote the projection onto $K$,
$$
\Pi_K(y) = \mathrm{arg\,min}_{x \in K} \|y - x\|,
$$
where $\|\cdot\|$ denotes the usual Euclidean ...
- 380
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54
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Number of indecomposable modules over representation-finite hereditary algebras
Let $A$ be a finite dimensional $K$-algebra over a field $K$ that is hereditary and of finite representation type.
It is well known that they are classified by Dynkin diagrams.
For algebraically ...
- 26.5k
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53
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References on a variant of Geometric Calculus
Geometric algebra and (standard) calculus, when synthesized, give rise to geometric calculus, a very powerful formalism.
I have read a bit about fractional calculus and time-scale calculus, both very ...
user537376
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28
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Analyzing simple DDE with simple characteristic test
I'm wondering if anyone can comment on the stability of delay DE given that we can analyze its characteristic equation.
For instance, let's say we have the DDE $\frac{d}{dt}x(t) = x(t-a),$ where $a$ ...
- 11
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86
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Uniqueness of compatible cycle decomposition for Eulerian trail
Fleischner mentions in his article Uniqueness of maximal dominating cycles in 3-regular graphs and of hamiltonian cycles in 4-regular graphs about the uniqueness of compatible cycle decomposition that ...
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73
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Regularity estimates of Double Layer potential
Let $\Omega$ is a bounded open subset of $\mathbb{R}^n,n\ge 2$ with $C^{\infty}$ boundary. Define $$I\left[ \phi \right](x) := -\frac{1}{\omega_n}\int_{\partial \Omega} \frac{(x-y)\cdot \nu_y}{|x-y|^n}...
- 69
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159
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Understanding the Hilbert scheme of subvarieties of $\mathbb{CP}^n$
EDIT: migrated to MSE.
I am looking to get a more concrete understanding of the Hilbert scheme of projective subvarieties, specifically over $\mathbb{C}$, and to obtain good references on this subject....
- 1,763
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0
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61
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A parabolic–hyperbolic in 3d: $\partial_t u(x,y,t)=\frac{1}{2}(\partial_{xx}u(x,y,t)-\partial_{yy}u(x,y,t))$
I was just wondering if somebody can provide some references for the parabolic–hyperbolic pde
$$\partial_t u(x,y,t)=\frac{1}{2}(\partial_{xx}u(x,y,t)-\partial_{yy}u(x,y,t)).$$
Apparently, the IVP ...
- 5,474
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0
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108
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looking for reference for two elliptic curves with equal formal group
I am looking for a reference.
In this post, @Chris Wurthrich made the following comment:
If the formal group laws (probably upon particular choice of coordinates) of two elliptic curves over any ring ...
- 195
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0
answers
34
views
Locally compact groupoid with range map restricted to isotropy groupoid is open
Suppose the action groupoid 𝐺=𝐻⋉𝑋, where 𝐻 is a locally compact group and 𝑋
a locally compact space is such that isotropy subgroups of H are isomorphic to each other.
Can this be an example of a ...
0
votes
0
answers
81
views
Computing elliptic periods from modular form
How are the periods of a modular elliptic curve computed as path integrals of its associated normalized weight 2 cusp form on the modular curve? Please provide specific paths for both periods and cite ...
- 2,907
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votes
0
answers
143
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Introductory resources on rewriting logic
Hi I would like to grasp the theory behind Maude [1], [2]
Are there any recommended video lecture notes, talks or introductory notes?
I have been exposed to Functional Analysis, Topology and some Term ...
