Factoriality conjecture for nodal complete intersection threefolds

Let $X$ be a nodal complete intersection threefold in $\mathbb{P}^5$ of hypersurfaces $F_n$ and $F_k$ of degrees $n$ and $k$, respectively, with $n\geq k$, and suppose that $F_k$ is smooth. Write $\operatorname{Sing}(X)$ for the singular locus of $X$. Factoriality conjecture. The threefold $X$ is $\mathbb{Q}$-factorial whenever

$$|\operatorname{Sing}(X)|\leq (n+k-2)(n+k-2)-1.$$

The conjecture is motivated by the sharp non-factorial example with $(n+k-2)^2$ nodes described immediately beforehand; the paper’s proven theorem gives the stronger numerical restriction $|\operatorname{Sing}(X)|\leq (n+k-2)(n-1)-1$, while the proposed bound remains to be established.