Singularities of Hermitian–Yang–Mills connections and Harder–Narasimhan–Seshadri filtrations
Singularities of Hermitian–Yang–Mills connections and Harder–Narasimhan–Seshadri filtrations
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Hermitian-Yang-Mills 连接和 Harder-Narasimhan-Seshadri 过滤的奇点
DOI：
10.1215/00127094-2020-0014
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Song Sun
中科院分区：
文献类型：
--
作者：
Xuemiao Chen;Song Sun
这是两篇论文中的第一篇，我们将厄米-杨-米尔斯连接的切锥在一个孤立的奇点上与底层自反层的复代数几何相关联，当层局部地建模于从射影空间拉回的全纯向量丛时。在本文中，我们将强加一个额外的假设，即由向量丛的Harder-Narasimhan-Seshadri滤子确定的分次层是自反的。一般来说，我们猜想切锥是由代数切锥的Harder-Narasimhan-Seshadri过滤唯一确定的，代数切锥是射影空间上的某个无挠层。当存在一个局部自由且稳定的代数切锥时，本文也证明了这个猜想。
This is the first of two papers where we relate tangent cones of Hermitian-Yang-Mills connections at an isolated singularity to the complex algebraic geometry of the underlying reflexive sheaf, when the sheaf is locally modelled on the pull-back of a holomorphic vector bundle from the projective space. In this paper we shall impose an extra assumption that the graded sheaf determined by the Harder-Narasimhan-Seshadri filtration of the vector bundle is reflexive. In general we conjecture that the tangent cone is uniquely determined by the Harder-Narasimhan-Seshadri filtration of an algebraic tangent cone, which is a certain torsion-free sheaf on the projective space. In this paper we also prove this conjecture when there is an algebraic tangent cone which is locally free and stable.
DOI：
10.1080/03605302.2018.1517792
发表时间：
2018-11-02
影响因子：
1.9
作者：
Jacob, Adam;Walpuski, Thomas
通讯作者：
Walpuski, Thomas