The generalized Franchetta conjecture for some hyper-Kahler varieties

Fu L, Laterveer R, Vial C, Shen M (2019)
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 130: 1-35.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor/in
Fu, Lie; Laterveer, Robert; Vial, CharlesUniBi; Shen, Mingmin
Abstract / Bemerkung
The generalized Franchetta conjecture for hyper-Kahler varieties predicts that an algebraic cycle on the universal family of certain polarized hyper-Keller varieties is fiberwise rationally equivalent to zero if and only if it vanishes in cohomology fiberwise. We establish Franchetta-type results for certain low (Hilbert) powers of low degree K3 surfaces, for the Beauville-Donagi family of Fano varieties of lines on cubic fourfolds and its relative square, and for 0-cycles and codimension-2 cycles for the Lehn-Lehn-Sorger-van Straten family of hyper-Kahler eightfolds. We also draw many consequences in the direction of the Beauville-Voisin conjecture as well as Voisin's refinement involving coisotropic subvarieties. In the appendix, we establish a new relation among tautological cycles on the square of the Fano variety of lines of a smooth cubic fourfold and provide some applications. (C) 2019 Elsevier Masson SAS. All rights reserved.
Stichworte
Algebraic cycles and Chow groups; Irreducible holomorphic symplectic; varieties; Moduli spaces; K3 surfaces; Cubic fourfolds
Erscheinungsjahr
2019
Zeitschriftentitel
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Band
130
Seite(n)
1-35
ISSN
0021-7824
eISSN
1776-3371
Page URI
https://pub.uni-bielefeld.de/record/2938383

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Fu L, Laterveer R, Vial C, Shen M. The generalized Franchetta conjecture for some hyper-Kahler varieties. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES. 2019;130:1-35.
Fu, L., Laterveer, R., Vial, C., & Shen, M. (2019). The generalized Franchetta conjecture for some hyper-Kahler varieties. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 130, 1-35. doi:10.1016/j.matpur.2019.01.018
Fu, L., Laterveer, R., Vial, C., and Shen, M. (2019). The generalized Franchetta conjecture for some hyper-Kahler varieties. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 130, 1-35.
Fu, L., et al., 2019. The generalized Franchetta conjecture for some hyper-Kahler varieties. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 130, p 1-35.
L. Fu, et al., “The generalized Franchetta conjecture for some hyper-Kahler varieties”, JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, vol. 130, 2019, pp. 1-35.
Fu, L., Laterveer, R., Vial, C., Shen, M.: The generalized Franchetta conjecture for some hyper-Kahler varieties. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES. 130, 1-35 (2019).
Fu, Lie, Laterveer, Robert, Vial, Charles, and Shen, Mingmin. “The generalized Franchetta conjecture for some hyper-Kahler varieties”. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 130 (2019): 1-35.