Algebraic Cycles on a Generalized Kummer Variety
Algebraic Cycles on a Generalized Kummer Variety
复制标题
广义 Kummer 簇上的代数循环
DOI：
10.1093/imrn/rnw266
复制
发表时间：
2018
影响因子：
1
通讯作者：
Xu Ze
中科院分区：
文献类型：
--
作者：
Xu Ze
我们明确计算任何广义库默簇与任何阿贝尔曲面的周动机。实际上，它属于由基础交换曲面的Chow动机生成的Chow动机范畴的刚性张量子范畴。这个计算的一个应用是表明霍奇猜想对广义库默簇的任意乘积成立。作为另一个应用，证明了广义库默簇的任意乘积上的所有数值平凡1-圈都是smash-幂零的.
We compute explicitly the Chow motive of any generalized Kummer variety associated to any abelian surface. In fact, it lies in the rigid tensor subcategory of the category of Chow motives generated by the Chow motive of the underlying abelian surface. One application of this calculation is to show that the Hodge conjecture holds for arbitrary products of generalized Kummer varieties. As another application, all numerically trivial 1-cycles on arbitrary products of generalized Kummer varieties are smash-nilpotent.