The generalized Franchetta conjecture for some hyper-Kähler varieties, II
Fu, Lie
Fu
Lie
Laterveer, Robert
Laterveer
Robert
Vial, Charles
Vial
Charles
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.
8
1065-1097
1065-1097
Ecole Polytechnique
2021