Moduli of cubic surfaces and their anticanonical divisors

Patricio Gallardo, Jesus Martinez-Garcia

Research output: Contribution to journalArticle

Abstract

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
Volume32
Issue number3
Early online date25 Feb 2019
DOIs
Publication statusPublished - 1 Sep 2019

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Datasets

Variations of GIT quotients package v0.6.13

Martinez Garcia, J. (Creator) & Gallardo, P. (Creator), University of Bath, 12 Dec 2017

Dataset

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