Compactness for $$\Omega $$-Yang–Mills connections
Compactness for $$\Omega $$-Yang–Mills connections
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$$Omega $$-YangâMills 连接的紧凑性
DOI：
10.1007/s00526-021-02178-0
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发表时间：
2022
影响因子：
2.1
通讯作者：
Wentworth, Richard A.
中科院分区：
文献类型：
--
作者：
Chen, Xuemiao;Wentworth, Richard A.
在维黎曼流形上，我们将已知的关于Yang-Mills联络的分析结果推广到一类称为-Yang-Mills联络的联络上，其中存在一个光滑的，不一定闭合的形式。特例包括一般复流形上的-反自对偶联络和Hermitian-Yang-Mills联络。通过一个重要的观察，得到了曲率一致有界的光滑-杨-Mills联络的模空间的一个弱紧性结果，并在一般复流形上的Hermtian-Yang-Mills联络的情况下得到了改进。证明了具有小能量集中的平凡丛上奇异-Yang-Mills联络的一个可去奇性定理。作为应用，给出了如何在一类Hodge-Riemann型平衡流形上的酉丛上紧化光滑Hermitian-Yang-Mills联络的模空间。这一类包括来自多极化的度量，特别是Kähler度量。在射影代数流形上的多极化情形下，具有固定行列式模规范变换的光滑不可约Hermitian-Yang-Mills联络的紧化继承了代数几何考虑的复杂结构。
On a Riemannian manifold of dimensionnwe extend the known analytic results on Yang–Mills connections to the class of connections called-Yang–Mills connections, whereis a smooth, not necessarily closed,-form onM. Special cases include-anti-self-dual connections and Hermitian–Yang–Mills connections over general complex manifolds. By a key observation, a weak compactness result is obtained for moduli space of smooth-Yang–Mills connections with uniformlybounded curvature, and it can be improved in the case of Hermitian–Yang–Mills connections over general complex manifolds. A removable singularity theorem for singular-Yang–Mills connections on a trivial bundle with small energy concentration is also proven. As an application, it is shown how to compactify the moduli space of smooth Hermitian–Yang–Mills connections on unitary bundles over a class of balanced manifolds of Hodge-Riemann type. This class includes the metrics coming from multipolarizations, and in particular, the Kähler metrics. In the case of multipolarizations on a projective algebraic manifold, the compactification of smooth irreducible Hermitian–Yang–Mills connections with fixed determinant modulo gauge transformations inherits a complex structure from algebro-geometric considerations.