All Questions
Tagged with singularity-theory stratifications
8 questions
6
votes
2
answers
1k
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Stratified pseudomanifold
In the definition of an $n$-dimensional stratified pseudomanifold one demands the following filtration
$X=X_n \supset X_{n-1}=X_{n-2} \supset X_{n-3}\supset ... \supset X_0 \supset X_{-1}=\emptyset$. ...
- 63.9k
6
votes
1
answer
475
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Whitney stratification of algebraic varieties
When do the orbits of an action on an algebraic variety make a Whitney stratification?
- 7,320
1
vote
0
answers
30
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Stratification which makes the defining functions isotrivial
Let $0\in X\subset\mathbb{C}^N$ be a germ of complex space and $0\in Z\subset X$ be a closed analytic subset (globally) defined by holomorphic functions $f_1,\dots,f_r$. Is there a complex analytic ...
- 1,102
7
votes
1
answer
372
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Non-example for Whitney (a) stratifications
Given a $C^1$ stratification $\mathscr{S}$ of a $C^1$ manifold $M$, we write $N^\ast \mathscr{S}$ for the union of conormals to the strata. The stratification is said to be Whitney (a) if $N^\ast \...
CommunityBot
- 1
4
votes
2
answers
737
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Whitney Conditions vs Equisingularity
In studying singular spaces, it is often important to pick an appropriate stratification which encodes the singularity structure. One class of such stratifications are called "Whitney stratifications" ...
- 7,320
6
votes
1
answer
2k
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Stratification of complex algebraic varieties
Let $V$ be a complex quasi-projective variety, we know from H. Whitney's and B Teissier works on stratifications of algebraic varieties that $V$ has an intrinsic stratification
$$X_0\subset X_2\...
- 2,554
7
votes
1
answer
574
views
Iterated Milnor fibrations and Thom's a_f condition
Ok so there's a lot of litterature about nearby cycles functor since it was introduced by Grothendieck and Deligne but I couldn't find any clear answer to the following natural question:
Problem: Let ...
- 146
5
votes
0
answers
344
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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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