论文标题
Koszul的拆分定理和超级Atiyah班
Koszul's Splitting Theorem and the Super Atiyah Class
论文作者
论文摘要
在本文中，我们介绍了复杂超级体的两个重要结果的独立叙述：（1）Koszul的分裂定理和（2）Donagi和Witten对超级Atiyah类的分解。这些结果与同样的圆形矢量束上的全球溶性连接与该矢量束的Atiyah类“相关”的意义相同 - 后者是对前者存在的障碍。在复杂的超级几何中：Koszul的定理与超级男性裂片的存在有关，而超级Atiyah类则涉及与分裂的存在有关的障碍。
In this article we present a self-contained account of two important results in complex supergeometry: (1) Koszul's Splitting theorem and (2) Donagi and Witten's decomposition of the super Atiyah class. These results are related in the same sense that global holomorphic connections on a holomorphic vector bundle are `related' to the Atiyah class of that vector bundle---the latter being the obstruction to the existence of the former. In complex supergeometry: Koszul's theorem pertains to the existence of supermanifold splittings whereas the super Atiyah class accordingly pertains to obstructions to the existence of splittings.
