Special cubic fourfolds, K3 surfaces and the Franchetta property - Archive ouverte HAL
Article Dans Une Revue International Mathematics Research Notices Année : 2021

Special cubic fourfolds, K3 surfaces and the Franchetta property

Lie Fu

Résumé

O'Grady conjectured that the Chow group of 0-cycles of the generic fiber of the universal family over the moduli space of polarized K3 surfaces of genus g is cyclic. This so-called generalized Franchetta conjecture has been solved only for low genera where there is a Mukai model (precisely, when g<11 and g=12, 13, 16, 18, 20), by the work of Pavic--Shen--Yin. In this paper, as a non-commutative analog, we study the Franchetta property for families of special cubic fourfolds (in the sense of Hassett) and relate it to O'Grady's conjecture for K3 surfaces. Most notably, by using special cubic fourfolds of discriminant 26, we prove O'Grady's generalized Franchetta conjecture for g=14, providing the first evidence beyond Mukai models.
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Dates et versions

hal-03621579 , version 1 (23-10-2024)

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Lie Fu, Robert Laterveer. Special cubic fourfolds, K3 surfaces and the Franchetta property. International Mathematics Research Notices, In press, ⟨10.1093/imrn/rnac102⟩. ⟨hal-03621579⟩
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