Stability Properties of Moduli Spaces
Stability Properties of Moduli Spaces
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DOI：
10.1090/noti2452
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发表时间：
2022-01
影响因子：
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通讯作者：
Rita Jiménez Rolland;Jenny Wilson
中科院分区：
文献类型：
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作者：
Rita Jiménez Rolland;Jenny Wilson
1.模空间和稳定模空间是拓扑或几何数据的参数化空间。它们经常出现在家庭中;例如，固定流形中n点的位形空间，R∞中d维线性子空间的Grassmannian空间，亏格g的Riemann曲面的模空间Mg.这些族通常由一些几何定义的量来索引，例如配置中的点数n，线性子空间的维数d，或黎曼曲面的亏格g。在过去的60年里，理解这些空间的拓扑结构一直是人们强烈兴趣的主题。对于模空间{Xn}n族，我们问：
1. Moduli Spaces and Stability Moduli spaces are spaces that parameterize topological or geometric data. They often appear in families; for example, the configuration spaces of n points in a fixed manifold, the Grassmannians of linear subspaces of dimension d in R∞, and the moduli spaces Mg of Riemann surfaces of genus g. These families are usually indexed by some geometrically defined quantity, such as the number n of points in a configuration, the dimension d of the linear subspaces, or the genus g of a Riemann surface. Understanding the topology of these spaces has been a subject of intense interest for the last 60 years. For a family of moduli spaces {Xn}n we ask: