紧凑型超Riemann Surfaces的一般族
Versal Families of Compact Super Riemann Surfaces
摘要：
我们称每一个复连通（1，1）维超流形为超Riemann曲面，并构造了紧超曲面的超族，其中底空间可以是包含所有复超流形的某些戴环空间.此外，我们还在所有超对称超族中选择了最大的超对称子超族。在特殊因子发生的情况下，我们证明了不存在的超族，而不是构建局部完全的。为了更精确地研究超对称超族，我们引入了紧超Riemann曲面超族范畴的协变对合对偶函子，并证明了超对称超族本质上是自对偶超族.作为分类结果的一个应用，它表明，在一个超对称超族的紧凑的超黎曼曲面局部在基地的超对称性是唯一确定的自同构与身份作为身体的拉回。
英文摘要：
We call every complex connected (1,1)-dimensional supermanifold a super Riemann surface and construct versal super families of compact ones, where the base spaces are allowed to be certain ringed spaces including all complex supermanifolds. Furthermore we choose maximal supersymmetric sub super families which turn out to be versal among all supersymmetric super families. In the cases where special divisors occur we prove the non-existence of versal super families and instead construct locally complete ones. For an accurate study of supersymmetric super families we introduce the duality functor, a covariant involution of the category of super families of compact super Riemann surfaces, and show that the supersymmetric super families are essentially the self-dual ones. As an application of the classification results it is shown that on a supersymmetric super family of compact super Riemann surfaces locally in the base the supersymmetry is uniquely determined up to pullback by automorphisms with identity as body.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
