The generalized Franchetta conjecture for some hyper-Kähler varieties, II

Fu L, Laterveer R, Vial C (2021)
Journal de l'École Polytechnique — Mathématiques 8: 1065-1097.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Fu, Lie; Laterveer, Robert; Vial, CharlesUniBi
Alternativer Titel
La conjecture de Franchetta généralisée pour certaines variétés hyper-kählériennes, II
Abstract / Bemerkung
We prove the generalized Franchetta conjecture for the locally complete family of hyper-Kahler eightfolds constructed by Lehn-Lehn-Sorger-van Straten (LLSS). As a corollary, we establish the Beauville-Voisin conjecture for very general LLSS eightfolds. The strategy consists in reducing to the Franchetta property for relative fourth powers of cubic fourfolds, by using the recent description of LLSS eightfolds as moduli spaces of Bridgeland semistable objects in the Kuznetsov component of the derived category of cubic fourfolds, together with its generalization to the relative setting due to Bayer-Lahoz-Macri-Nuer-Perry-Stellari. As a by-product, we compute the Chow motive of the Fano variety of lines on a smooth cubic hypersurface in terms of the Chow motive of the cubic hypersurface.
Stichworte
Chow ring; motives; hyper-Kahler varieties; cubic hypersurfaces; Franchetta conjecture; Beauville-Voisin conjecture; derived categories; stability conditions; Kuznetsov component; moduli space of sheaves; tautological ring
Erscheinungsjahr
2021
Zeitschriftentitel
Journal de l'École Polytechnique — Mathématiques
Band
8
Seite(n)
1065-1097
ISSN
2429-7100
eISSN
2270-518X
Page URI
https://pub.uni-bielefeld.de/record/2957075

Zitieren

Fu L, Laterveer R, Vial C. The generalized Franchetta conjecture for some hyper-Kähler varieties, II . Journal de l'École Polytechnique — Mathématiques. 2021;8:1065-1097.
Fu, L., Laterveer, R., & Vial, C. (2021). The generalized Franchetta conjecture for some hyper-Kähler varieties, II . Journal de l'École Polytechnique — Mathématiques, 8, 1065-1097. https://doi.org/10.5802/jep.166
Fu, L., Laterveer, R., and Vial, C. (2021). The generalized Franchetta conjecture for some hyper-Kähler varieties, II . Journal de l'École Polytechnique — Mathématiques 8, 1065-1097.
Fu, L., Laterveer, R., & Vial, C., 2021. The generalized Franchetta conjecture for some hyper-Kähler varieties, II . Journal de l'École Polytechnique — Mathématiques, 8, p 1065-1097.
L. Fu, R. Laterveer, and C. Vial, “The generalized Franchetta conjecture for some hyper-Kähler varieties, II ”, Journal de l'École Polytechnique — Mathématiques, vol. 8, 2021, pp. 1065-1097.
Fu, L., Laterveer, R., Vial, C.: The generalized Franchetta conjecture for some hyper-Kähler varieties, II . Journal de l'École Polytechnique — Mathématiques. 8, 1065-1097 (2021).
Fu, Lie, Laterveer, Robert, and Vial, Charles. “The generalized Franchetta conjecture for some hyper-Kähler varieties, II ”. Journal de l'École Polytechnique — Mathématiques 8 (2021): 1065-1097.

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