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Moduli of cubic surfaces and their anticanonical divisors

Gallardo, Patricio and Martinez-Garcia, Jesus (2019) 'Moduli of cubic surfaces and their anticanonical divisors.' Revista Matemática Complutense, 32 (3). 853 - 873. ISSN 1139-1138

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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.

Item Type: Article
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 30 Aug 2019 15:59
Last Modified: 30 Aug 2019 15:59

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