The compactifications of moduli spaces of Burniat surfaces with $2\leq K^{2}\leq5$

TL;DR

This paper studies the compactifications of moduli spaces for Burniat surfaces with specific invariants by incorporating KSBA surfaces, providing a detailed description of their boundary components.

Contribution

It introduces new compactifications of moduli spaces of Burniat surfaces using KSBA theory, extending previous classifications for these surfaces.

Findings

Description of boundary components of moduli spaces

Construction of compactified moduli spaces with KSBA surfaces

Extension of known classifications for Burniat surfaces

Abstract

We describe compactifications of moduli spaces of Burniat surfaces with $2\leq K_{X}^{2}\leq5$ obtained by adding KSBA surfaces, i.e. slc surfaces $X$ with ample canonical class $K_{X}$.