On asymptotic bounds for the number of irreducible components of the   moduli space of surfaces of general type
  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. We obtain a higher growth then the previous growth by Manetti [M97]. 
Michael L\"onne and Matteo Penegini
math.AG