Kodaira dimension of moduli of special cubic fourfolds
-
Sho Tanimoto
and
Anthony Várilly-Alvarado
Abstract
A special cubic fourfold is a smooth hypersurface of degree 3 and dimension 4 that contains a surface not homologous to a complete intersection. Special cubic fourfolds give rise to a countable family of Noether–Lefschetz divisors
Funding statement: Tanimoto was partially supported by Lars Hesselholt’s Niels Bohr Professorship. Várilly-Alvarado was supported by NSF grant DMS-1103659 and NSF CAREER grant DMS-1352291.
Acknowledgements
We are grateful to Brendan Hassett for many conversations where he patiently answered our questions, and for his constant encouragement. We thank Klaus Hulek for an illuminating discussion at the Simons Symposium “Geometry over Non-Closed Fields” in March of 2015. We also thank an anonymous referee for their careful reading of the manuscript, and for pertinent suggestions that improved the exposition of the paper. Computer calculations were carried out in Magma [5].
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Weak approximation for isotrivial families
- Genus of abstract modular curves with level-ℓ structures
- Strong shift equivalence and algebraic K-theory
- The solvable length of groups of local diffeomorphisms
- Positivity properties of metrics and delta-forms
- Iwasawa theory for the symmetric square of a modular form
- Cohomology and torsion cycles over the maximal cyclotomic extension
- Integrability of continuous bundles
- Kodaira dimension of moduli of special cubic fourfolds
Articles in the same Issue
- Frontmatter
- Weak approximation for isotrivial families
- Genus of abstract modular curves with level-ℓ structures
- Strong shift equivalence and algebraic K-theory
- The solvable length of groups of local diffeomorphisms
- Positivity properties of metrics and delta-forms
- Iwasawa theory for the symmetric square of a modular form
- Cohomology and torsion cycles over the maximal cyclotomic extension
- Integrability of continuous bundles
- Kodaira dimension of moduli of special cubic fourfolds
