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。
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英文标题:
《Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks》
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作者:
Fabio Nironi
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最新提交年份:
2009
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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
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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
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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}.
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PDF链接:
https://arxiv.org/pdf/0811.1949