阻塞加厚与超流形
Obstructed Thickenings and Supermanifolds
摘要：
与任何超流形相关联的是空间的过滤，称为加厚。这是本文的目的是研究他们到一定的等价，然后同构的复解析设置。我们从两个角度研究它们：（1）作为嵌入在超流形中的结构和（2）抽象。在整个过程中，我们将以澄清和解决以下问题为目标：给定的增厚何时嵌入到超流形中？这个问题，从本质上讲，是伊斯特伍德和勒布朗首先研究的。在这篇文章中，我们开始与他们的研究教学帐户，之后，我们进一步研究超几何中的加厚，并提出了一个给定的顺序加厚的分类。作为对我们研究的补充，我们评论了复超流形的模问题，并考虑了加厚的类似问题。最后，为了说明本文中的思想，我们通过描述复射影平面的一些受阻加厚来结束。
英文摘要：
Associated to any supermanifold is a filtration by spaces, referred to as thickenings. It is the objective of this article to study them up to a certain equivalence and then up to isomorphism in the complex-analytic setting. We study them from two points of view: (1) as structures embedded in supermanifolds and (2) abstractly. Throughout, we will be guided by the goal to clarify and address the question: when does a given thickening embed in a supermanifold? Such a question was, in essence, first studied by Eastwood and LeBrun. In this article we begin with a pedagogical account of their study, after which we further study thickenings in supergeometry and present a classification of thickenings of a given order. As a complement to our study, we comment on the moduli problem for complex supermanifolds and consider the analogous problem for thickenings. Finally, to illustrate the ideas in this article, we conclude by describing some obstructed thickenings of the complex projective plane.
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