Explicit compactifications of moduli spaces of Campedelli and Burniat surfaces

TL;DR

This paper explicitly constructs geometric compactifications of moduli spaces for Campedelli and Burniat surfaces, adding stable surfaces with ample canonical class to understand their boundary behavior.

Contribution

It provides explicit descriptions of compactifications for specific moduli spaces of surfaces of general type, focusing on Campedelli and Burniat surfaces.

Findings

Explicit geometric compactifications described.

Stable surfaces with ample canonical class added.

Boundary components characterized for these moduli spaces.

Abstract

We describe explicitly the geometric compactifications, obtained by adding slc surfaces $X$ with ample canonical class, for two connected components in the moduli space of surfaces of general type: Campedelli surfaces with $\pi_1(X)=\mathbb Z_2^3$ and Burniat surfaces with $K^2=6$.