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

TL;DR

This paper studies how the number of irreducible components in the moduli space of certain algebraic surfaces grows asymptotically, revealing a faster growth rate than previously known for specific families of surfaces.

Contribution

It provides new asymptotic bounds for the growth of irreducible components in the moduli space of surfaces of general type, focusing on surfaces isogenous to a higher product with a specific group.

Findings

Higher asymptotic growth rate than earlier estimates

Focus on surfaces with group (Z/2Z)^k

Improved bounds for the number of components

Abstract

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 $(\mathbb Z/2\mathbb Z)^k$. We obtain a significantly higher growth than the one in our previous paper [LP14, arXiv:1402.6438].