摘要翻译：
本文引入了具有射影模格式的tame Deligne-Mumford叠上相干束的Gieseker稳定性的概念，并在Olsson和Starr引用{MR2007396}的意义下选择了叠上的生成束。我们证明了这个稳定性条件是开的，纯维半可定束形成一个有界族。我们将半可定滑轮的模叠加显式构造为有限型全局商，并以Simpson引用的开创性论文{MR1307297}的精神研究了稳定滑轮的模格式及其自然紧致性。利用这种通用机制，我们可以作为特例，检索Lieblich引用{MR2309155}和Yoshioka引用{MR2306170}关于扭曲滑轮模和Maruyama-Yokogawa在{MR1162674}中引入的抛物稳定性的结果。
---
英文标题：
《Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks》
---
作者：
Fabio Nironi
---
最新提交年份：
2009
---
分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--
一级分类：Mathematics        数学
二级分类：Commutative Algebra        交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
--

---
英文摘要：
  We introduce a notion of Gieseker stability for coherent sheaves on tame Deligne-Mumford stacks with projective moduli scheme and some chosen generating sheaf on the stack in the sense of Olsson and Starr \cite{MR2007396}. We prove that this stability condition is open, and pure dimensional semistable sheaves form a bounded family. We explicitly construct the moduli stack of semistable sheaves as a finite type global quotient, and study the moduli scheme of stable sheaves and its natural compactification in the same spirit as the seminal paper of Simpson \cite{MR1307297}. With this general machinery we are able to retrieve, as special cases, results of Lieblich \cite{MR2309155} and Yoshioka \cite{MR2306170} about moduli of twisted sheaves and parabolic stability introduced by Maruyama-Yokogawa in \cite{MR1162674}.
---
PDF链接：
https://arxiv.org/pdf/0811.1949