Motives and the Pfaffian-Grassmannian equivalence

Laterveer, Robert

doi:10.48550/arxiv.2105.03171

Cited by 1 publication

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References 32 publications

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“…By Theorem 1.5, it follows from the Franchetta property for special cubic fourfolds in C 14 , which has just been proved. (We remark that instead of appealing to the general result Theorem 1.5, the second author has established in [Lat21,Corollary 4.4] directly the link between the CH 1 of a Pfaffian cubic fourfold and the CH 0 of the associated K3 surface, which is generically defined. This avoids the use of techniques from derived categories.…”

Section: Franchetta For C 20mentioning

confidence: 99%

Special cubic fourfolds, K3 surfaces and the Franchetta property

Fu,

Laterveer

2021

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LIE FU AND ROBERT LATERVEERABSTRACT. 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 socalled generalized Franchetta conjecture has been solved only for low genera where there is a Mukai model (precisely, when g ≤ 10 and g = 12, 13, 16, 18, 20), by the work of Pavic-Shen-Yin. In this paper, as a non-commutative analogue, 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. CONTENTS L| Ct ≃ ω ⊗mCt , for some m ∈ Z. Franchetta's conjecture was proved by Harer [Har83] (see also [AC87] and [Mes87]).

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Section: Franchetta For C 20mentioning

confidence: 99%