Calderón-Moreno et al.'s LCT implies strong Euler homogeneity conjecture for free divisors

Let $D$ be a free divisor in a complex manifold $X$. The logarithmic comparison conjecture. If the logarithmic comparison theorem holds for $D$, then $D$ is strongly Euler homogeneous. This is a proposed higher-dimensional converse to the implication that local quasi-homogeneity implies the logarithmic comparison theorem; the converse is stated to be an open problem.