自反层上的典则度量及相关热流的研究

发布时间：2018-01-06 21:11

本文关键词：自反层上的典则度量及相关热流的研究　出处：《中国科学技术大学》2017年博士论文　论文类型：学位论文

【摘要】：本文主要研究自反层上典则度量结构的存在性问题和其上Hermitian-Yang-Mills热流的收敛性问题。在论文的第一部分中,我们研究紧致Kahler流形上更为一般的半稳定自反Higgs层。我们证明半稳定自反Higgs层上必存在渐近Hermitian-Einstein度量结构。作为应用,我们在紧致Kahler流形的半稳定自反Higgs层上建立了Bogomolov型陈数不等式。在论文的第二部分中,我们研究自反层上Hermitian-Yang-Mills热流的收敛性问题。我们证明任取一时间子列Hermitian-Yang-Mills热流所对应的陈联络在附加一系列规范变换后,在一个Hausdorff余维数至少为4的紧集之外,必局部光滑收敛于Yang-Mills联络,该极限联络所决定的全纯丛必可延拓成整体的自反层。最后我们证明延拓后的极限自反层和原自反层的Harder-Narasimhan-Seshadri滤过的二次对偶是同构的。该结果回答了 Bando和萧荫堂于上世纪九十年代所提的一个问题。
[Abstract]:In this paper, we mainly study the existence of the reflexive supercanonical metric structure and the convergence of the Hermitian-Yang-Mills heat flux on it. In the first part of this paper. We study a more general semi-stable reflexive Higgs layer on a compact Kahler manifold. We prove that there must be asymptotic Hermitian-Einstei on a semi-stable reflexive Higgs layer. N metric structure. As an application. In the second part of this paper, we establish the Bogomolov type Chen number inequality on the semi-stable reflexive Higgs layer of compact Kahler manifolds. We study the convergence of the Hermitian-Yang-Mills heat flux on the reflexive layer. We prove that the Hermitian-Yang-Mills heat flux can be subsequenced at any time. The corresponding Chen connection is attached to a series of specifications. In addition to a compact set in which the Hausdorff codimension is at least 4, it must be locally smooth to converge to the Yang-Mills connection. The holomorphic cluster determined by the limit connection can be extended into a global reflexive layer. Finally, we prove the extended limit reflexive layer and the Harder-Narasimhan-Seshadr of the original reflexive layer. The quadratic duality of I filter is isomorphic. A question raised by Bando and Xiao Yin-tang in -10s.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O186.1

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