Let $X\subset \mathbb C^n$ be a complex hypersurface (given by $F=0$ where $F$ is a polynomial). It is known then that $X$ admits *a* Whitney stratification. This is a decomposition of $X$ into smooth submanifolds (strata) that have some adjacency properties (Whitney conditions a and b).


**Question.** Does $X$ have a *minimal* stratification, i.e. such a stratification that for any other Whitney stratification of $X$ the strata of the *minimal* one are unions of the strata of the other one?


At least maybe this is known for varieties with certain type of singularities?



Is there a "minimal" Whitney stratification of a complex hypersurface?
The answer is yes for any reduced equidimensional analytic space. This is the proposition 3.2 (and remark after the proof) page 479 of [Variétés polaires II](https://webusers.imj-prg.fr/%7Ebernard.teissier/documents/VarPol2.pdf) by Bernard Teissier.


