Moduli of cubic surfaces and their anticanonical divisors

Patricio Gallardo, Jesus Martinez-Garcia

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2 Citations (SciVal)


We consider the moduli space of log smooth pairs formed by a cubic surface and an anticanonical divisor. We describe all compactifications of this moduli space which are constructed using geometric invariant theory and the anticanonical polarization. The construction depends on a weight on the divisor. For smaller weights the stable pairs consist of mildly singular surfaces and very singular divisors. Conversely, a larger weight allows more singular surfaces, but it restricts the singularities on the divisor. The one-dimensional space of stability conditions decomposes in a wall-chamber structure. We describe all the walls and relate their value to the worst singularities appearing in the compactification locus. Furthermore, we give a complete characterization of stable and polystable pairs in terms of their singularities for each of the compactifications considered.

Original languageEnglish
Pages (from-to)853-873
Number of pages21
JournalRevista Matemática Complutense
Issue number3
Early online date25 Feb 2019
Publication statusPublished - 1 Sept 2019


  • Classification of singularities
  • Cubic surfaces
  • Fano varieties
  • Geometric invariant theory
  • Moduli of pairs

ASJC Scopus subject areas

  • General Mathematics


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