Chern forms of singular metrics on vector bundles
Chern forms of singular metrics on vector bundles
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向量丛上奇异度量的 Chern 形式
DOI：
10.1016/j.aim.2017.12.009
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发表时间：
2016
影响因子：
1.7
通讯作者：
Martin L. Sera
中科院分区：
文献类型：
--
作者：
Richard Larkang;Hossein Raufi;J. Ruppenthal;Martin L. Sera
我们研究了全纯向量束上的奇异厄密度量，遵循bernttson - pourun。Raufi之前的工作表明，对于这样的度量，通常不可能将曲率定义为具有测量系数的电流。在本文中，我们证明了尽管如此，在度量的奇异集上适当的余维限制下，仍然可以将Chern形式定义为局部有限质量的0阶闭合电流，它表示向量束的Chern类。
We study singular hermitian metrics on holomorphic vector bundles, following Berndtsson–Păun. Previous work by Raufi has shown that for such metrics, it is in general not possible to define the curvature as a current with measure coefficients. In this paper we show that despite this, under appropriate codimension restrictions on the singular set of the metric, it is still possible to define Chern forms as closed currents of order 0 with locally finite mass, which represent the Chern classes of the vector bundle.