Duke Mathematical Journal
- Duke Math. J.
- Volume 163, Number 10 (2014), 1885-1927.
Hodge theory and derived categories of cubic fourfolds
Cubic fourfolds behave in many ways like surfaces. Certain cubics—conjecturally, the ones that are rational—have specific surfaces associated to them geometrically. Hassett has studied cubics with surfaces associated to them at the level of Hodge theory, and Kuznetsov has studied cubics with surfaces associated to them at the level of derived categories.
These two notions of having an associated surface should coincide. We prove that they coincide generically: Hassett’s cubics form a countable union of irreducible Noether–Lefschetz divisors in moduli space, and we show that Kuznetsov’s cubics are a dense subset of these, forming a nonempty, Zariski-open subset in each divisor.
Duke Math. J., Volume 163, Number 10 (2014), 1885-1927.
First available in Project Euclid: 8 July 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
Secondary: 14J35: $4$-folds 14J10: Families, moduli, classification: algebraic theory 14J28: $K3$ surfaces and Enriques surfaces
Addington, Nicolas; Thomas, Richard. Hodge theory and derived categories of cubic fourfolds. Duke Math. J. 163 (2014), no. 10, 1885--1927. doi:10.1215/00127094-2738639. https://projecteuclid.org/euclid.dmj/1404824304