论文标题
某些超级kähler品种的广义弗朗切塔（Franchetta）猜想，ii
The generalized Franchetta conjecture for some hyper-Kähler varieties, II
论文作者
论文摘要
我们证明了由Lehn-Lehn-Sorger-Van Straten（LLSS）构建的Hyper-Kähler八倍的本地完整家族的广义弗朗切塔猜想。作为推论，我们为非常普通的LLSS八倍建立了Beauville-Voisin猜想。该策略包括通过将LLSS八倍的最新描述用作kuznetsov中可在可半固定物体的模量的描述来减少到Franchetta属性的相对第四幂，以构成可在kuznetsov的模量空间。作为副产品，我们根据立方超表面的Chow动机来计算平滑的立方体表面上的Fano各种线的Chow动机。
We prove the generalized Franchetta conjecture for the locally complete family of hyper-Kähler 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 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-Macrì-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.
