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October 2015 Singular hermitian metrics on holomorphic vector bundles
Hossein Raufi
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Ark. Mat. 53(2): 359-382 (October 2015). DOI: 10.1007/s11512-015-0212-4

Abstract

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 Θh 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 Θh. 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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Hossein Raufi. "Singular hermitian metrics on holomorphic vector bundles." Ark. Mat. 53 (2) 359 - 382, October 2015. https://doi.org/10.1007/s11512-015-0212-4

Information

Received: 9 January 2014; Revised: 3 February 2015; Published: October 2015
First available in Project Euclid: 30 January 2017

zbMATH: 1345.32021
MathSciNet: MR3391176
Digital Object Identifier: 10.1007/s11512-015-0212-4

Rights: 2015 © Institut Mittag-Leffler

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Vol.53 • No. 2 • October 2015
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