论文标题
关于阿贝尔品种的周期类别和亚伯 - 雅各比的几何形状
Cycle classes on abelian varieties and the geometry of the Abel-Jacobi map
论文作者
论文摘要
我们讨论了一个阿贝里亚品种的两个特性，即是雅各布人的产物和“分裂”较弱的属性的直接总结。我们将第一个属性与Abelian品种的曲线类别的曲线类别相关联。我们还将这两种属性与阿伯利亚品种上的brauer-severi品种上的通用零循环的存在问题联系起来。对于立方三倍的普遍编成2周期的存在问题也建立了类似的关系。
We discuss two properties of an abelian variety, namely, being a direct summand in a product of Jacobians and the weaker property of being "split". We relate the first property to the integral Hodge conjecture for curve classes on abelian varieties. We also relate both properties to the existence problem for universal zero-cycles on Brauer-Severi varieties over abelian varieties. A similar relation is established for the existence problem of a universal codimension 2 cycle on a cubic threefold.
