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Singular hermitian metrics on holomorphic vector bundles

Hossein Raufi Department of Mathematics Chalmers Institute of Technology, and University of Gothenburg

Complex Variables and Complex Analysis Differential Geometry mathscidoc:1701.08013

Arkiv for Matematik, 53, (2), 359-382, 2014.1
We introduce and study the notion of singular hermitian metrics on holomorphic vector bundles, following Berndtsson and Păun. We define what it means for such a metric to be positively and negatively curved in the sense of Griffiths and investigate the assumptions needed in order to locally define the curvature Θ^{$h$}as a matrix of currents. We then proceed to show that such metrics can be regularised in such a way that the corresponding curvature tensors converge weakly to Θ^{$h$}. Finally we define what it means for$h$to be strictly negatively curved in the sense of Nakano and show that it is possible to regularise such metrics with a sequence of smooth, strictly Nakano negative metrics.
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@inproceedings{hossein2014singular,
  title={Singular hermitian metrics on holomorphic vector bundles},
  author={Hossein Raufi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203641065568087},
  booktitle={Arkiv for Matematik},
  volume={53},
  number={2},
  pages={359-382},
  year={2014},
}
Hossein Raufi. Singular hermitian metrics on holomorphic vector bundles. 2014. Vol. 53. In Arkiv for Matematik. pp.359-382. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203641065568087.
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