Milnor–Tjurina conjecture for non-complete-intersection surface singularities in C4

Let $(V,0)$ be a normal surface singularity in $\mathbb C^4$ that is not a complete intersection. Milnor–Tjurina conjecture in C4.

$$\mu\geq \tau-1,$$

with equality if and only if $(V,0)$ is quasi-homogeneous. The claim concerns the non-Gorenstein determinantal case, where the semi-universal deformation has smooth base and $\alpha=0$. The source presents it as an open conjecture following discussion of the difficulty of computing the Milnor number.