On asymptotic bounds for the number of irreducible components of the moduli space of surfaces of general type II

In this paper we investigate the asymptotic growth of the number of irreducible and connected components of the moduli space of surfaces of general type corresponding to certain families of surfaces isogenous to a higher product with group $(\mathbb{Z}\mathrm{/}2\mathbb{Z}{)}^k$. We obtain a significantly higher growth than the one in our previous paper [LP14, arXiv:1402.6438].