Explicit compactifications of moduli spaces of Campedelli and Burniat surfaces

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 $K^2=6$.

v.4: Minor update: (1) In the symmetry group of Burniat configuration (Thm. 2) GL(2,F_2) replaced by C_3. (2) In the surface on the right in Fig. 10 (E degeneration), the colors rotated cyclically; similarly in Fig. 12 (EF degeneration)