arXiv 1503.054782015-03-18math.AG

光滑Deligne-Mumford叠加的“自底向上”刻画

A "bottom up" characterization of smooth Deligne-Mumford stacks

Anton Geraschenko, Matthew Satriano

备注：: arXiv admin note: text overlap with arXiv:1201.4807

摘要：

在不经意的讨论中，一个栈经常被描述为一个变种（粗糙空间），以及附着在它的一些子变种上的稳定器组。但是，此描述并不唯一指定堆栈。我们的主要结果表明，对于一个大类的堆栈通常会遇到，这种描述确实表征他们。此外，我们证明，每个这样的堆栈可以描述在两个简单的程序迭代应用到其粗糙的空间：规范堆栈建设和根堆栈建设。更确切地说，如果$\mathcal X$是一个光滑分离的驯服Deligne-Mumford堆栈有限型域$k$平凡一般稳定，它是完全由其粗空间$X$和分歧因子（$X$上）的粗空间态射$π\colon \mathcal X \to X$。因此，要指定这样的堆栈，只需指定余维1点的稳定器的种类和顺序。然后，确定基团结构以及较高余维点的稳定基团。

英文摘要：

In casual discussion, a stack is often described as a variety (the coarse space) together with stabilizer groups attached to some of its subvarieties. However, this description does not uniquely specify the stack. Our main result shows that for a large class of stacks one typically encounters, this description does indeed characterize them. Moreover, we prove that each such stack can be described in terms of two simple procedures applied iteratively to its coarse space: canonical stack constructions and root stack constructions. More precisely, if $\mathcal X$ is a smooth separated tame Deligne-Mumford stack of finite type over a field $k$ with trivial generic stabilizer, it is completely determined by its coarse space $X$ and the ramification divisor (on $X$) of the coarse space morphism $π\colon \mathcal X \to X$. Therefore, to specify such a stack, it is enough to specify a variety and the orders of the stabilizers of codimension 1 points. The group structures, as well as the stabilizer groups of higher codimension points, are then determined.

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。

摘要：

英文摘要：

相关论文