Strong tangency conjecture for separatrices of non-dicritical foliations

Let $X$ be a quasi-compact complex manifold, let $\mathcal{F}$ be a codimension-$1$ foliation on $X$ given by an algebraic $1$-form, and let $Z$ be the union of its separatrices. Strong tangency conjecture. If $\mathcal{F}$ is non-dicritical, then $Z$ is strongly tangent to $\mathcal{F}$. This conjecture is identified as the key condition on which the existence of a resolution in the non-dicritical case depends; the source states that it is equivalent to every non-dicritical foliation being totally separable, but does not give a resolution.