Open Access
Translator Disclaimer
January, 2003 Residues of Chern classes
Tatsuo SUWA
J. Math. Soc. Japan 55(1): 269-287 (January, 2003). DOI: 10.2969/jmsj/1196890854


If we have a finite number of sections of a complex vector bundle E over a manifold M, certain Chern classes of E are localized at the singular set S, i.e., the set of points where the sections fail to be linearly independent. When S is compact, the localizations define the residues at each connected component of S by the Alexander duality. If M itself is compact, the sum of the residues is equal to the Poincaré dual of the corresponding Chern class. This type of theory is also developed for vector bundles over a possibly singular subvariety in a complex manifold. Explicit formulas for the residues at an isolated singular point are also given, which express the residues in terms of Grothendieck residues relative to the subvariety.


Download Citation

Tatsuo SUWA. "Residues of Chern classes." J. Math. Soc. Japan 55 (1) 269 - 287, January, 2003.


Published: January, 2003
First available in Project Euclid: 5 December 2007

zbMATH: 1094.14500
MathSciNet: MR1939197
Digital Object Identifier: 10.2969/jmsj/1196890854

Primary: 14C17 , 32A27 , 57R20
Secondary: 14B05 , 32S05

Keywords: Chern classes , frames of vector bundles , Grothendieck residues relative to subvarieties , Localization

Rights: Copyright © 2003 Mathematical Society of Japan


Vol.55 • No. 1 • January, 2003
Back to Top