摘要翻译：
推广Klyachko和Perling的工作，我们得到了任意非奇异toric簇$x$上任意维数纯等变束的组合描述。利用几何不变理论(GIT)，这允许我们在$x$共表示自然模函子上构造纯等变束的显式模空间（类似于Payne在等变向量束情况下的工作）。代数环面在$x$上的作用提升到$x$上所有Gieseker稳定束的模空间，我们用$x$上纯等变束的模空间显式地表示它的不动点轨迹。其中一个问题是在GIT问题的一侧寻找一个等变线丛，它精确地恢复Gieseker稳定性。在无扭转等变束的情况下，我们总是可以构造这样的等变线束。作为副产品，我们得到了$\mu$-稳定自反束模空间在$x$上的不动点轨迹的组合描述。作为一个应用，我们在续篇中展示了如何用这些方法来计算非奇异完全曲面上稳定的无扭槽的模空间的Euler特征的母函数。
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英文标题：
《Fixed point loci of moduli spaces of sheaves on toric varieties》
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作者：
Martijn Kool
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最新提交年份：
2014
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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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英文摘要：
  Extending work of Klyachko and Perling, we develop a combinatorial description of pure equivariant sheaves of any dimension on an arbitrary nonsingular toric variety $X$. Using geometric invariant theory (GIT), this allows us to construct explicit moduli spaces of pure equivariant sheaves on $X$ corepresenting natural moduli functors (similar to work of Payne in the case of equivariant vector bundles). The action of the algebraic torus on $X$ lifts to the moduli space of all Gieseker stable sheaves on $X$ and we express its fixed point locus explicitly in terms of moduli spaces of pure equivariant sheaves on $X$. One of the problems arising is to find an equivariant line bundle on the side of the GIT problem, which precisely recovers Gieseker stability. In the case of torsion free equivariant sheaves, we can always construct such equivariant line bundles. As a by-product, we get a combinatorial description of the fixed point locus of the moduli space of $\mu$-stable reflexive sheaves on $X$. As an application, we show in a sequel how these methods can be used to compute generating functions of Euler characteristics of moduli spaces of $\mu$-stable torsion free sheaves on nonsingular complete toric surfaces.
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PDF链接：
https://arxiv.org/pdf/0810.0418