论文标题
关于Hyper-kähler品种的异性动机
On the birational motive of hyper-Kähler varieties
论文作者
论文摘要
我们引入了一种新的升序过滤，我们将共同激进的过滤与共同代数的基本理论相比，在尖的光滑射击品种的食物组上。对于投影型Hyper-Kähler歧管上的零循环，我们猜想它与Voisin引入的过滤一致。这是针对K3表面上稳定物体的模量空间，通用的Kummer品种以及平滑立方四倍的Fano品种的各种线的。我们的总体策略是将平稳的投射品种的异性动机视为对角线嵌入的共核对象，并在上述情况下显示出所谓的严格分级，其相关的过滤与Voisin的过滤一致。作为独立兴趣的结果，我们通过表面的异性动机确定了某些投射性超kähler歧管的异性动机，以升级为Voisin Voisin的“表面分解”概念，并表明某些投射性超kähler歧管的异性动机是作为共核对象的。我们还将我们的共同自由基过滤在亚伯族品种的食物基团上与博维尔的特征空间分解联系起来。
We introduce a new ascending filtration, that we call the co-radical filtration in analogy with the basic theory of co-algebras, on the Chow groups of pointed smooth projective varieties. In the case of zero-cycles on projective hyper-Kähler manifolds, we conjecture it agrees with a filtration introduced by Voisin. This is established for moduli spaces of stable objects on K3 surfaces, for generalized Kummer varieties and for the Fano variety of lines on a smooth cubic fourfold. Our overall strategy is to view the birational motive of a smooth projective variety as a co-algebra object with respect to the diagonal embedding and to show in the aforementioned cases the existence of a so-called strict grading whose associated filtration agrees with the filtration of Voisin. As results of independent interest, we upgrade to rational equivalence Voisin's notion of "surface decomposition" and show that the birational motive of some projective hyper-Kähler manifolds is determined, as a co-algebra object, by the birational motive of a surface. We also relate our co-radical filtration on the Chow groups of abelian varieties to Beauville's eigenspace decomposition.
