论文标题
较难的纳拉西姆汉多边形和大量法律
Harder-Narasimhan polygons and Laws of Large Numbers
论文作者
论文摘要
我们以Codogni和Patakfalvi的最新技术为基础，来自\ cite {Codogni：Patakfalvi：2021}，这些技术用于建立有关Chow Mumford Line Bundles的$ \ k $ semistable Fano fano Verieties的定理。在这里，我们应用了中心极限定理来确定\ emph {Hunder和Narasimhan多边形}顶点的渐近概率性质。作为我们主要结果的应用，我们使用它来建立\ cite {codogni：patakfalvi：2021}的主要技术结果的过滤矢量空间类似物。在这样做的过程中，我们扩展了坡度稳定性理论，对于过滤的向量空间，这是由Faltings和Wüstholz\ cite {faltings {faltings：wustholz}引发的。我们对\ emph {Harder和Narasimhan Data}的抽象研究的灵感来源是我们在这里定义的概念，是Grayson \ Cite \ Cite {Grayson：1984}的晶格还原方法。另一个是Faltings和Wüstholz的作品，\ cite {faltings：wustholz}，以及Evertse和Ferretti，\ cite {Evertse：ferretti：2013}，它在投影型品种的二聚体近似值之内。
We build on the recent techniques of Codogni and Patakfalvi, from \cite{Codogni:Patakfalvi:2021}, which were used to establish theorems about semi-positivity of the Chow Mumford line bundles for families of $\K$-semistable Fano varieties. Here we apply the Central Limit Theorem to ascertain the asymptotic probabilistic nature of the vertices of the \emph{Harder and Narasimhan polygons}. As an application of our main result, we use it to establish a filtered vector space analogue of the main technical result of \cite{Codogni:Patakfalvi:2021}. In doing so, we expand upon the slope stability theory, for filtered vector spaces, that was initiated by Faltings and Wüstholz \cite{Faltings:Wustholz}. One source of inspiration for our abstract study of \emph{Harder and Narasimhan data}, which is a concept that we define here, is the lattice reduction methods of Grayson \cite{Grayson:1984}. Another is the work of Faltings and Wüstholz, \cite{Faltings:Wustholz}, and Evertse and Ferretti, \cite{Evertse:Ferretti:2013}, which is within the context of Diophantine approximation for projective varieties.
