关于Orbifold子结构的继承
On the Inheritance of Orbifold Substructures
摘要：
在上一篇文章中，我们定义了一个非常灵活的子轨道的概念，并描述了那些可以作为轨道嵌入的图像出现的子轨道。特别是，子轨道是轨道嵌入的图像，当它们饱和和分裂时。本文讨论了三个orbifold $\mathcal{Q}\subset\mathcal{P}\subset\mathcal{O}$的orbifold结构继承问题。我们确定了一个有吸引力的，但最终不充分的概念，继承典型orbifold子结构。特别地，我们给出了一个具体的例子，其中$\mathcal{Q}$的orbifold结构是从$\mathcal{P}$正则遗传的，并且$\mathcal{P}$的orbifold结构是从$\mathcal{O}$正则遗传的，但是$\mathcal{Q}$的orbifold结构不是从$\mathcal{O}$正则遗传的。另一方面，很容易看出，当$\mathcal{Q}$嵌入到$\mathcal{P}$中，而$\mathcal{P}$嵌入到$\mathcal{O}$中时，所有的规范继承的orbifold子结构将一致。我们还调查在这种情况下的饱和度的属性，并给出一个例子的suborbifold与规范orbifold子结构是不饱和的。
英文摘要：
In a previous article, we defined a very flexible notion of suborbifold and characterized those suborbifolds which can arise as the images of orbifold embeddings. In particular, suborbifolds are images of orbifold embeddings precisely when they are saturated and split. This article addresses the problem of orbifold structure inheritance for three orbifolds $\mathcal{Q}\subset\mathcal{P}\subset\mathcal{O}$. We identify an appealing but ultimately inadequate notion of an inherited canonical orbifold substructure. In particular, we give a concrete example where the orbifold structure of $\mathcal{Q}$ is canonically inherited from $\mathcal{P}$, and the orbifold structure of $\mathcal{P}$ is canonically inherited from $\mathcal{O}$, but the orbifold structure of $\mathcal{Q}$ is not canonically inherited from $\mathcal{O}$. On the other hand, it is easy to see that when $\mathcal{Q}$ is embedded in $\mathcal{P}$, and $\mathcal{P}$ is embedded in $\mathcal{O}$, all of the canonical inherited orbifold substructures will agree. We also investigate the property of saturation in this context, and give an example of a suborbifold with the canonical orbifold substructure that is not saturated.
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