复曲面DM堆栈、伪加权射影空间和标记剪切单形的惯性群
Inertia groups of a toric DM stack, fake weighted projective spaces, and labelled sheared simplices
摘要：
本文确定了复曲面Deligne-Mumford栈[Z/G]（在光滑流形范畴上考虑）上的点的惯性群（迷向群），该栈是由利用stacky fan或stacky多面体的商构造实现的.该计算提供了某些几何数据和组合数据之间的明确对应。特别是，我们获得了一个计算的连接组件的身份元素$G_0 \subset G$和组件组$G/G_0$在底层stacky风扇，使我们能够表征复曲面DM堆栈，这是全球性的一致性。作为另一个应用程序，我们得到的堆叠多面体的特征，产生堆栈相当于加权投影堆栈，更一般地说，“假”加权投影堆栈。最后，我们详细说明了我们的结果在特殊情况下的标签剪切单纯形，明确的计算可以在方面的标签。
英文摘要：
This paper determines the inertia groups (isotropy groups) of the points of a toric Deligne-Mumford stack [Z/G] (considered over the category of smooth manifolds) that is realized from a quotient construction using a stacky fan or stacky polytope. The computation provides an explicit correspondence between certain geometric and combinatorial data. In particular, we obtain a computation of the connected component of the identity element $G_0 \subset G$ and the component group $G/G_0$ in terms of the underlying stacky fan, enabling us to characterize the toric DM stacks which are global quotients. As another application, we obtain a characterization of those stacky polytopes that yield stacks equivalent to weighted projective stacks and, more generally, to `fake' weighted projective stacks. Finally, we illustrate our results in detail in the special case of labelled sheared simplices, where explicit computations can be made in terms of the facet labels.
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。
