Chern forms of singular metrics on vector bundles

被引：10

作者：

Larkang, Richard ^{[1
,2
]}

Raufi, Hossein ^{[1
,2
]}

Ruppenthal, Jean ^{[3
]}

Sera, Martin ^{[1
,2
]}

机构：

[1] Chalmers Univ Technol, Dept Math, S-41296 Gothenburg, Sweden

[2] Univ Gothenburg, S-41296 Gothenburg, Sweden

[3] Univ Wuppertal, Dept Math, Gaussstr 20, D-42119 Wuppertal, Germany

来源：

ADVANCES IN MATHEMATICS | 2018年 / 326卷

基金：

瑞典研究理事会;

关键词：

Singular hermitian metrics; Holomorphic vector bundles; Chern classes; Segre forms; HERMITIAN METRICS;

D O I：

10.1016/j.aim.2017.12.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study singular hermitian metrics on holomorphic vector bundles, following Berndtsson-Paun. 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. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：465 / 489

页数：25

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