Chern Forms of Hermitian Metrics with Analytic Singularities on Vector Bundles
Journal article, 2022
We define Chern and Segre forms, or rather currents, associated with a Griffiths positive singular Hermitian metric h with analytic singularities on a holomorphic vector bundle E. The currents are constructed as pushforwards of generalized Monge-Ampere products on the projectivization of E. The Chern and Segre currents represent the Chern and Segre classes of E, respectively, and coincide with the Chern and Segre forms of E and h where h is smooth. Moreover, our currents coincide with the Chern and Segre forms constructed by the first three authors and Ruppenthal in the cases when these are defined.
Author
Richard Lärkäng
University of Gothenburg
Chalmers, Mathematical Sciences, Algebra and geometry
Hossein Raufi
Chalmers, Mathematical Sciences, Algebra and geometry
University of Gothenburg
Martin Sera
Kyoto University of Advanced Science
Elizabeth Wulcan
University of Gothenburg
Chalmers, Mathematical Sciences, Algebra and geometry
Indiana University Mathematics Journal
0022-2518 (ISSN)
Vol. 71 5 153-189Subject Categories
Algebra and Logic
Geometry
Mathematical Analysis
DOI
10.1512/iumj.2022.71.8834