Chern forms of singular metrics on vector bundles
Artikel i vetenskaplig tidskrift, 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

Författare

Richard Lärkäng

Chalmers, Matematiska vetenskaper, Algebra och geometri

Göteborgs universitet

Hossein Raufi

Chalmers, Matematiska vetenskaper, Algebra och geometri

Göteborgs universitet

Jean Ruppenthal

Bergische Universität Wuppertal

Martin Sera

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Algebra och geometri

Advances in Mathematics

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

Vol. 326 465-489

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.1016/j.aim.2017.12.009