All Questions
Tagged with dg.differential-geometry singularity-theory
21 questions with no upvoted or accepted answers
7
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0
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483
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Theories of manifolds w/ extra structure and singularities
Many different objects in mathematics can be described as manifolds with extra structure. Among the most famous examples of these are smooth manifolds, Riemannian manifolds, complex manifolds, and ...
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7
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0
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229
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Higher homotopy of diffeomorphism groups from singularities
In the case of a genus $g$ surface $\Sigma$, it is well known that $MCG(\Sigma) = \pi_0 \operatorname{Diff}^+(\Sigma)$ is generated by Dehn twists, which come from a Kahler degeneration with smooth ...
- 1,981
6
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0
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95
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forms on singular spaces that can be integrated on an LCI
I'd like to characterize rational $k$-forms on a singular scheme $X$ which can be integrated on any (real) bounded submanifold that is locally LCI in $X$ in a real sense (i.e., which is the real ...
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6
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376
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Topological Singularities in Affine Varieties
Let $X$ be an affine variety over $\mathbb{C}$. Let $x\in X$.
If $x$ is non-singular, then $x$ is locally holomorphic (in the Euclidean topology). See here for a relevant MO post.
By results of ...
- 8,529
5
votes
0
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343
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Stratification of a smooth map
So, this is an exercise. But from math.stackexchange I have been suggested to post this question here.
To find the Thom-Boardman stratification of the smooth map
$f(x,y,a,b,c,d)=x^2y+y^3+a(x^2+y^2)+...
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4
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0
answers
127
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Geometric interpretations of $A_k$ singularities on plane curves
Definition: A real smooth analytic function $f$ defined on some neighborhood of $t_0$ is said to have an $A_k$ singularity at $t_0$ if and only if $$ f'(t_0) = f''(t_0) = \dots = f^{(k)}(t_0) = 0$$ ...
4
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0
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247
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H-principle for smoothing
I'm trying to find algebraic embedding of singular curves into projective varieties that can be smoothed symplectically but not algebraically.
It's not hard (e.g. using the methods in Hartshorne-...
- 1,981
3
votes
0
answers
206
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An upper bound for the number of singularities of a transversal vector field isometric to the zero field
Let $(M,g)$ be a Riemannian manifold. We equip the tangent bundle $TM$ with the Sasaki metric $g_s$.
A smooth vector field $X:M \to TM$ is called a transversal vector field if $X(M)$ is transverse ...
- 356
3
votes
0
answers
146
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Frobenius structure for A_n singularities
I need to compute monodromy matrices $M(v)$, associated to a Frobenius structure for $A_n$ singularity with flat coordinates $v_1,\dots,v_n$, that is, $f(x)=x^{n+1}$. (due to Saito, Dubrovin etc.) ...
- 31
3
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0
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99
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Normal form of volume functional about a minimal surface
Let $S$ be a closed manifold and $(M,g)$ be a Riemannian manifold. Minimal submanifolds are by definition the critical points of the volume functional
$$F: \mathcal{Imm}(S,M) \to \mathbb{R} \qquad \...
- 5,824
2
votes
0
answers
95
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Non-compactness on Penrose singularity
I've been studying singularities in GR, and (obviously), came across PST.
Let us state it as the following:
Let $(M, g)$ be a connected globally hyperbolic
spacetime with a noncompact Cauchy ...
- 125
2
votes
0
answers
128
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Making a continuous function into embedding by adding additional dimension
While doing my researches, I encountered the following problem.
Let $f:[0,1]^n\rightarrow \mathbb{R}^{n+k}$ be an arbitrary continuous function.
I want to make this function an embedding by perturbing ...
- 173
2
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0
answers
191
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Blowing up the zero section for "Chasse au Canard" (some new kind of geometric canards)
In this paper "Canard cycles and center manifolds" one encounters the blowing up of a non isolated set or manifold of singularities of a vector field or a singular foliation. This is a ...
- 356
2
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0
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111
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About the regularity of Thom's first isotopy theorem
Consider an abstract stratified set $(V, \Sigma)$ in the sense of Thom-Mather
(see Mather's note page 491-492 https://www.ams.org/journals/bull/2012-49-04/S0273-0979-2012-01383-6/S0273-0979-2012-01383-...
- 83
2
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0
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510
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Weil Petersson metric on moduli space of Calabi Yau manifolds
Let $f:(X,D)\to Y$ be a holomorphic fibre space where $D$ is divisor with conic singularities and let fibres $(X_s,D_s)$ are log Calabi-Yau pair .i.e $K_X+D$ is nummerically trivial, then we have ...
user21574
1
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0
answers
52
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Making sense of constant scalar curvature metric horns
Suppose we have a compact oriented surface $S$ and we remove a point $p$ on it. We could consider a neighboorhood $U$ of the puncture $p$, so that the points in this neighboorhood are described by ...
1
vote
0
answers
105
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Codimension of cusp singularities in the space of 2-jets
In trying to prove Cerf's theorem about homotopies between Morse-functions I ended up thinking about the following problem.
For $n>2$, $a= (a_{i,j})\in GL(n-2)$, we define the polynomial map $C_a:\...
- 2,533
1
vote
0
answers
67
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Robust features intuition?
The terminology robust features was introduced by Ian Porteous as they are features of a surface wich be followed when the surface is deformed. They capture important aspects of the surface geometry. ...
- 119
1
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0
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218
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Desingularization of the zero section of $TM$ as the manifold of singularities of the geodesic flow
However the method of "Blowing up of singularities" is initially introduced for an isolated singularity, but this method have been generalized to blowing up of a "Manifold of singularities"...
- 356
0
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0
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121
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Is any singularity a subgerm of $(\mathbb{C}^n, 0)$?
I am studying singularity theory. I have often come across, in the literature, the sentence which says "let $(X,0) \subset (\mathbb{C}^n,0)$ be a singularity". Here a singularity is a ...
- 369
0
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0
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228
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On Whitney's paper on real algebraic varieties
I had previously asked this question on math.stackexchange and did not receive an answer and so I decided to reword it and pose it here.
This question is based on Whitney's paper titled "...
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