Unanswered Questions
51,795 questions with no upvoted or accepted answers
2
votes
0
answers
37
views
What are the terms in the Eagon Northcott complex?
Let $E \to F$ be a map of vector bundles on a scheme $X$ of ranks $e, f$ (actually, I hope $X$ may be a stack here). Suppose $e \leq f$. I want to describe the locus $D \subseteq X$ where $E \to F$ ...
- 1,154
4
votes
0
answers
37
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Examples of cocomplete categories without equalizers
What are some examples of cocomplete categories without equalizers? And what are some examples of cocomplete categories without binary products?
They must exist, but at the moment I don't know any. Of ...
- 66.2k
0
votes
0
answers
30
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Interpretations of the tangent Chern numbers of the complex projective spaces $CP^n$?
I've identified the generating functions for the tangent Chern numbers of the complex projective spaces $CP^n$ given in "Algebraic topology of the Lagrange inversion" by Victor Buchstaber ...
- 11.2k
1
vote
0
answers
56
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Does a continuous variation through compact $n$ dim manifolds preserve topology?
I begin by writing the definition below that tries to capture what a continuous family /path of manifolds is. The underlying motivation behind the definition is that the transition maps should be ...
- 1,441
2
votes
0
answers
52
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Triangulated manifolds with local orientation reversal
For a (smoothly) triangulated $n$ manifold $M$, I'll say that the triangulation is amphichiral if it admits an orientation-reversing automorphism. I'll say that the triangulation is locally ...
- 239
0
votes
0
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37
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Explosion of the moment of double stochastic exponential
We consider the stochastic system
$$\frac{dS_t}{S_t}=-R_t\,dW_t,$$
with
$$dR_t=-R_t\,dt-R_t\,dW_t, \quad R_0>0.$$
We conjecture, and would like to show that
$$\mathbb{E}[S_t^2]
=
S_0^2\,\mathbb{E}\...
- 696
0
votes
0
answers
84
views
System of divergence free vector fields
Let $\Omega \subset \mathbb R^p$ be a convex, bounded domain with a smooth boundary. Let $a_{ij} : \Omega \to \mathbb R_+$ be a non-negative smooth function for $i, j \in \{1, 2\}.$ I am interested in ...
- 14.2k
1
vote
0
answers
38
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Number of connected acyclic gentle tree algebras
Let $X_n$ denote the number of acyclic connected gentle tree algebras (given by quiver and admissible relations over a field) with $n$ simple modules. Those are also exactly the connected quiver ...
- 28.5k
5
votes
0
answers
82
views
Constructive status of the meta-theory of intuitionistic propositional logic
Intuitionistic propositional logic has several kinds of models. Bezhanishvili and Holliday [1] showed that these models form a neat hierarchy:
Kripke
Beth
Topological
Dragalin
Heyting
in the order ...
- 150
0
votes
0
answers
25
views
A problem about the vector-valued error estimate for multivariate Hermite interpolation
I am reading an Hermite interpolation method on manifold which is in Section4 in HERE, the core idea is as follows.
Set $dim(\mathcal{M})=m$. We construct an interpolation $\hat{f}_{\tan }: \mathbb{R}^...
- 1,051
1
vote
0
answers
40
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Tail log-convexity of moments of an even Hermite polynomial of a Gaussian
Let $G\sim N(0,1)$ and let $\{\mathrm{He}_n\}_{n\ge 0}$ denote the probabilists' Hermite polynomials.
Let $H_n:=\mathrm{He}_n/\sqrt{n!}$ be the orthonormal version, so that
$\mathbb{E}[H_n(G)H_m(G)]=\...
- 73
2
votes
0
answers
43
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Non-admissible variation mixed Hodge structure
As is well-known, admissiblity plays an important role in mixed Hodge theory. I am wondering if there are some explicit examples of variation of mixed Hodge structure on a smooth open variety, even an ...
- 113
4
votes
0
answers
52
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Structure of residually nilpotent groups with nilpotent quotients
Let $G$ be a finitely generated, residually finite, and residually nilpotent group. Suppose $G$ satisfies the following properties:
Every proper quotient of $G$ is virtually nilpotent with Hirsch ...
- 1,219
3
votes
0
answers
65
views
Computing all graph homomorphisms of two graphs
Is there any software that, given two graphs $G$ and $H$, can compute all graph homomorphisms from $G$ to $H$?
I found this rather old question, but it does not seem to answer my query.
It could be ...
- 1,434
7
votes
0
answers
69
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Does the category of lucid presheaves form a cocompletion under a class of colimits?
Following Freyd in Several new concepts: Lucid and concordant functors, pre-limits, pre-completeness, the continuous and concordant completions of categories, call a presheaf $P : \mathbf A^{\text{op}}...
- 12.9k