embedded ${\mathbb Q}$-resolution of $Y \subset S$, we will compute $g$ *weighted blow-ups*. After each blow-up, we will be able to eliminate one variable so that we obtain a situation very similar to the one we have started with, but with one equation in $Y$ and $S$ less. Therefore, in the last step, the problem will have been reduced to the resolution of a cusp in a Hirzebruch-Jung singularity of type $\frac{1}{d}(1,q)$, which can be solved with a single weighted blow-up. One can compare this process to the resolution of an irreducible plane curve with $g$ Puiseux pairs using toric modifications; after each weighted blow-up, the number of Puiseux pairs is lowered by one and the last step coincides with the resolution of an irreducible plane curve with one Puiseux pair. Our case, however, will be more challenging as the strict transform of $Y$ after the first blow-up will pass in general through the singular locus of the ambient space. The resulting ${\mathbb Q}$-resolution is described in Theorem \[thm:resolutionY\], and its resolution graph is a tree as in Figure \[fig:dual-graph\]. Stratifying the exceptional divisor of the resolution such that the multiplicity is constant along each stratum and computing the Euler 