My main focus is on the applications of stratification in complex/abstract Algebraic geometry especially, from the scheme-theoretic viewpoint and (Added) Moduli spaces. I have a vague feeling that ...
Let $X$ be a smooth $k-$ variety and $F$ a coherent sheaf on it. One knows that the sheaf of differentials $\Omega^1_X$ of $X$ is locally free. Hence one has by standard isomorphisms $Hom(F,F\otimes ...