论文标题
Hitchin-Simpson方程的解决方案序列的行为
The behavior of sequences of solutions to the Hitchin-Simpson equations
论文作者
论文摘要
Hitchin-Simpson方程是由连接和HIGGS字段组成的一对的一阶非线性方程。在本文中，我们研究了Hitchin-Simpson方程的解决方案序列的行为，其封闭的Kähler歧管具有无限的Higgs字段$ L^2 $规范。我们证明了连接和重新归一化的Higgs领域的紧凑性结果，该田地概括了Taubes和Mochizuki的工作。 作为应用程序，我们证明了Kähler歧管上的每一个$ \ mathbb {z}/2 $谐波1形，可以变形为Hitchin-Simpson方程的一系列解决方案。此外，我们在任何Kähler歧管上解决了广义Hitchin的WKB问题。
The Hitchin-Simpson equations are first-order non-linear equations for a pair consisting of a connection and a Higgs field. In this paper, we study the behavior of sequences of solutions to the Hitchin-Simpson equations on closed Kähler manifolds with unbounded $L^2$ norms of the Higgs fields. We prove a compactness result for the connections and renormalized Higgs fields, which generalizes the work of Taubes and Mochizuki. As applications, we prove that every $\mathbb{Z}/2$ harmonic 1-form on a Kähler manifold can be deformed into a sequence of solutions to the Hitchin-Simpson equations. Additionally, we solve the generalized Hitchin's WKB problem on any Kähler manifold.
