Let $C$ be an algebraic curve (one dimensional projective regular connected scheme of finite type) of genus $g$ over an algebraically closed field $k$ with structure morphism $\pi$. By Riemann-Roch, the global sections of the sheaf of differentials $\Omega$ are a $g$-dimensional vectorspace over $k$ and every element $\omega \in \Omega(C)$ has exactly $2g-2$ zeroes (counted with multiplicity). Therefore the vector bundle $V = \mathcal{Spec} (\pi_* \Omega)$ over $\operatorname{Spec}(k)$ can be naturally decomposed by the order of the zeroes of the differentials, i.e. for every partition of $2g-2$ into nonnegative integers one can form the subset of differentials such that the orders of the zeroes give the same partition.

My guess is, that this is not just a decomposition set theoretically, but actually a decomposition in locally closed subsets and therefore a stratification (using the induced reduced structure). Naively for every subset one wants that some zeros agree (a closed condition) and some do not agree (an open condition) but I seem to be unable to make this rigorous.