a very difficult approach and we refer it to future works. In this paper, a large section is dedicated to check several matching of (stringy) Hodge numbers in the case of projective hypersurfaces of non-negative Kodaira dimension (see §\[sez:ipersuperfici\]). One side of this check (we call $A$-side) turns out to be easily computable (Theorem \[thm:m\*=k\]). The other side of this check (so called $B$-side) is sensibly more intricate, requiring the introduction of suitable partial Gorenstein resolutions, on which studying and computing the involved stringy Hodge numbers (Theorems \[thm:B-mirror0\], \[thm:B-mirror1\] and \[thm:B-mirror2\]). Here, combinatorial computation are rather tricky (see §\[ssez:combinatorica\]). Notice that, the resolution process is quite more natural in the [Calabi-Yau ]{}case, as the [Calabi-Yau ]{}constraint imposes a sort of *canonical* resolutions, so called *maximal projective crepant partial (MPCP)* resolutions [@Batyrev94 Def. 2.2.13]. For Kodaira positive hypersurfaces, the choice of needed resolution is absolutely free, after one construct a suitable partial resolution of $\Q$-Gorenstien singularities to Gorenstein ones (Proposition \[prop:risoluzione\]). This fact makes such a $B$-side check a bit unsatisfactory, as one can go on by blowing up the mirror model, until $h^{1,1}$ reaches the desired value for obtaining a matching with the complex moduli number of the corresponding projective 