Explicit KSBA compactifications of moduli spaces of secondary and tertiary Burniat surfaces

TL;DR

This paper explicitly constructs KSBA compactifications of moduli spaces for Burniat surfaces with specific degrees, enriching the understanding of their geometric structure and boundary components.

Contribution

It provides explicit descriptions of KSBA compactifications for moduli spaces of Burniat surfaces with degrees 3, 4, and 5, focusing on surfaces with ample canonical class.

Findings

Explicit geometric descriptions of KSBA compactifications.

Identification of boundary components with slc surfaces.

Enhanced understanding of moduli space structures.

Abstract

We describe explicitly the geometric KSBA compactifications, obtained by adding slc surfaces~$X$ with ample canonical class, of moduli spaces of Burniat surfaces of degrees $K^2=5$, $4$ and $3$.