复曲面Deligne-Mumford堆之间的全局一致性
Global quotients among toric Deligne-Mumford stacks
摘要：
本文刻画了光滑商栈$[M/G]$中的全局商栈-与作用于流形的有限群相关联的光滑栈，其中$M$是李群$G$具有光滑真作用的光滑流形。该特征描述在$M$上的连通分量$G_0$的作用方面，并且与（堆叠）基本群和覆盖理论有关。这种表征，然后应用到光滑复曲面Deligne-Mumford堆栈，复曲面DM堆栈之间的全局一致性，然后其特征在于在其相关的组合数据的stacky风扇。
英文摘要：
This work characterizes global quotient stacks---smooth stacks associated to a finite group acting a manifold---among smooth quotient stacks $[M/G]$, where $M$ is a smooth manifold equipped with a smooth proper action by a Lie group $G$. The characterization is described in terms of the action of the connected component $G_0$ on $M$ and is related to (stacky) fundamental group and covering theory. This characterization is then applied to smooth toric Deligne-Mumford stacks, and global quotients among toric DM stacks are then characterized in terms of their associated combinatorial data of stacky fans.
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