The factoriality conjecture for nodal hypersurfaces in projective four-space

Let $V\subset\mathbb{P}^{4}$ be a hypersurface of degree $d$ with at most isolated ordinary double points, and let $\mathrm{Sing}(V)$ denote its singular locus. Factoriality conjecture. If

$$|\mathrm{Sing}(V)|<(d-1)^{2},$$

then $V$ is factorial. This extends the preceding factoriality result for double solids; the source gives no resolution of the conjecture in this generality.