Chern forms of singular metrics on vector bundles
Journal article, 2018

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.

Singular hermitian metrics

Segre forms

Holomorphic vector bundles

Chern classes

Author

Richard Lärkäng

Chalmers, Mathematical Sciences, Algebra and geometry

University of Gothenburg

Hossein Raufi

Chalmers, Mathematical Sciences, Algebra and geometry

University of Gothenburg

Jean Ruppenthal

Bergische Universität Wuppertal

Martin Sera

University of Gothenburg

Chalmers, Mathematical Sciences, Algebra and geometry

Advances in Mathematics

0001-8708 (ISSN) 1090-2082 (eISSN)

Vol. 326 465-489

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

DOI

10.1016/j.aim.2017.12.009

More information

Latest update

4/13/2018