The stratifications tag has no usage guidance.

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### Where should I look for computing the intersection homology of projective varieties?

I'm learning about intersection cohomology topologically through MacPherson's "New York Times Article". This is a very nice guide which gives a nice idea on how to use these methods for low-...

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### Sufficient conditions for a conormal vector to be regular for an orbit stratification

Let a complex reductive group $G$ act on a $\mathbb{C}^{n}$ with finitely many orbits. Let $\mathcal{S}$ be the stratification of $\mathbb{C}^{n}$ according to these orbits. Let $(x,\xi) \in T_S^{*}\...

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### Homotopy property of constructible sheaves on stratified spaces

Let $X$ be a stratified topological space (in my case $X$ is a compact space presented as a finite union of locally closed topological manifolds of finite dimension (strata) such that the closure of ...

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### Topology on the space of constructible sheaves

Let $X$ be a nice compact topological space with a fixed finite stratification by locally closed topological manifolds. At the beginning one may assume that $X$ is a complex algebraic manifold with ...

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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\...

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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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### 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 ...

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### intersection of Whitney stratifications

Let $X$ be an oriented smooth manifold with dimension $n$. If $U$ and $V$ are two oriented closed submanifolds of $X$ and $U$ is transverse to $V$ in $X$. Then $U\cap V$ (suppose the intersection is ...

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### transverse intersection of Whitney stratifications

Let $M$ be a smooth manifold. If $X$ and $Y$ are two Whitney objects, i.e. subsets with a given Whitney stratification, then $X$ and $Y$ are transverse if each stratum of $X$ is transverse to each ...

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### When a Whitney stratification has no stratum of codimension one?

Let $G$ be a compact Lie group, and $M$ be a smooth $n$-dimensional $G$-manifold which admits an orientation preserving the $G$-action. Then $M$ has a natural Whitney stratification induced by the ...

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### singular support of D-module smooth w.r.t. a stratification

(1) Suppose that $X$ is a smooth complex algebraic variety, stratified by some nice smooth stratification $S$. Let $M$ be a $D$-module on $X$, s.t. its shriek-pullback (or star... whatever is ...

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### Is the Alexander-Pontryagin duality applicable to stratified spaces

If $D$ is the discriminant of the space of all planar curves of a fixed degree, and $D'$ is the subspace whose only singularities are nodes or cusps, then is it possible to apply Alexander-Pontryagin ...