Hermitian Yang-Mills metrics on reflexive sheaves over asymptotically cylindrical Kahler manifolds
Hermitian Yang-Mills metrics on reflexive sheaves over asymptotically cylindrical Kahler manifolds
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DOI：
10.1080/03605302.2018.1517792
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发表时间：
2018-11-02
影响因子：
1.9
通讯作者：
Walpuski, Thomas
中科院分区：
文献类型：
--
作者：
Jacob, Adam;Walpuski, Thomas
我们证明了渐近圆柱(Acyl)Kahler流形上的Donaldson-Uhlenbeck-Yau定理的一个类比：如果是acyl Kahler流形上的一个渐近于u-稳定全纯向量丛的自反层，则它允许一个渐近平移不变的射影Hermite Yang-Mills度量(曲率在奇异集上)。我们的证明结合了Uhlenbeck和Yau的解析连续性方法和Bando和Siu提出的几何正则化方案。
We prove an analogue of the Donaldson-Uhlenbeck-Yau theorem for asymptotically cylindrical (ACyl) Kahler manifolds: If is a reflexive sheaf over an ACyl Kahler manifold, which is asymptotic to a mu-stable holomorphic vector bundle, then it admits an asymptotically translation-invariant projectively Hermitian Yang-Mills metric (with curvature in across the singular set). Our proof combines the analytic continuity method of Uhlenbeck and Yau with the geometric regularization scheme introduced by Bando and Siu.