论文标题
Weil类型和旋转图的四倍
Fourfolds of Weil type and the spinor map
论文作者
论文摘要
Markman和O'Grady的最新论文除了在Hodge的猜想和Hyperkaehler品种上的主要结果外，还提供了对Abelian四倍的Weil类型的家族的令人惊讶和明确的描述。他们还提供了一个新的观点，说明了以下事实，即这些Abelian品种是一定重量的Kuga satake品种，两个hodge结构排名第六。 在本文中，我们对这些结果进行了介绍。使用SO（8）的半旋转表示定义的旋转图。为简单起见，我们使用基本表示理论，并避免使用试验性。
Recent papers by Markman and O'Grady give, besides their main results on the Hodge conjecture and on hyperkaehler varieties, surprising and explicit descriptions of families of abelian fourfolds of Weil type with trivial discriminant. They also provide a new perspective on the well-known fact that these abelian varieties are Kuga Satake varieties for certain weight two Hodge structures of rank six. In this paper we give a pedestrian introduction to these results. The spinor map, which is defined using a half-spin representation of SO(8), is used intensively. For simplicity, we use basic representation theory and we avoid the use of triality.
