Explicit compactifications of moduli spaces of Campedelli and Burniat surfaces

Valery Alexeev; Rita Pardini

Explicit compactifications of moduli spaces of Campedelli and Burniat surfaces

Algebraic Geometry 2025-05-15 v4

Authors: Valery Alexeev , Rita Pardini

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 $K^2=6$ .

Keywords

campedelli surfaces burniat surfaces moduli spaces compactifications slc surfaces ample canonical class surfaces of general type

Cite

@article{arxiv.0901.4431,
  title  = {Explicit compactifications of moduli spaces of Campedelli and Burniat surfaces},
  author = {Valery Alexeev and Rita Pardini},
  journal= {arXiv preprint arXiv:0901.4431},
  year   = {2025}
}

Comments

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)

Explicit compactifications of moduli spaces of Campedelli and Burniat surfaces

Abstract

Keywords

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