Carlini–Catalisano–Geramita conjecture on generic disjoint unions of linear spaces

Let $X\subset\mathbb{P}^n$ be a generic union of linear spaces whose components are pairwise non-intersecting. Recall that $X$ has good postulation if, for every degree $d\geq 0$, it imposes the expected number of conditions on hypersurfaces of degree $d$; equivalently, one of $h^0(\mathcal{I}_X(d))$ and $h^1(\mathcal{I}_X(d))$ vanishes. Carlini–Catalisano–Geramita conjecture. The scheme $X$ has good postulation. This conjecture extends the known good-postulation results for generic points and generic unions of lines, including the Hartshorne–Hirschowitz theorem. Its resolution status is not specified in the supplied text.