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15 July 2014 Hodge theory and derived categories of cubic fourfolds
Nicolas Addington, Richard Thomas
Duke Math. J. 163(10): 1885-1927 (15 July 2014). DOI: 10.1215/00127094-2738639

Abstract

Cubic fourfolds behave in many ways like K3 surfaces. Certain cubics—conjecturally, the ones that are rational—have specific K3 surfaces associated to them geometrically. Hassett has studied cubics with K3 surfaces associated to them at the level of Hodge theory, and Kuznetsov has studied cubics with K3 surfaces associated to them at the level of derived categories.

These two notions of having an associated K3 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.

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Nicolas Addington. Richard Thomas. "Hodge theory and derived categories of cubic fourfolds." Duke Math. J. 163 (10) 1885 - 1927, 15 July 2014. https://doi.org/10.1215/00127094-2738639

Information

Published: 15 July 2014
First available in Project Euclid: 8 July 2014

zbMATH: 1309.14014
MathSciNet: MR3229044
Digital Object Identifier: 10.1215/00127094-2738639

Subjects:
Primary: 14F05
Secondary: 14J10, 14J28, 14J35

Rights: Copyright © 2014 Duke University Press

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Vol.163 • No. 10 • 15 July 2014
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