Stratum of holomorphic one-forms ($\mathcal{H}(k_1,\dots ,k_r)$)

The locus of nonzero holomorphic one-forms with a fixed list of zero multiplicities $k_1,\dots ,k_r$, summing to $2g-2$. The SL2R action on differentials preserves this list. For example $\mathcal{H}(2)$ and $\mathcal{H}(1,1)$ are distinct genus-two strata.