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.
Holomorphic vector bundles
Segre forms
Singular hermitian metrics
Chern classes
Author
Richard Lärkäng
University of Gothenburg
Chalmers, Mathematical Sciences, Algebra and geometry
Hossein Raufi
University of Gothenburg
Chalmers, Mathematical Sciences, Algebra and geometry
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. 326 465-489Subject Categories
Algebra and Logic
Geometry
Mathematical Analysis
DOI
10.1016/j.aim.2017.12.009