Vector Bundles and Chern Classes

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 2)


We will construct, for any vector bundle E on a scheme X, Chern class operations
$$c_{i}\left ( E \right)\cap \_:A_{k}\,X\rightarrow A_{k-i}\,X,$$
satisfying properties expected from topology. From the special case of line bundles done in § 2.5, we first construct inverse Chern classes, or Segre classes, which are then inverted to produce Chern classes. The first Chern class operations are also used to describe A * E and A * P (E) in terms of A * X.


Exact Sequence Vector Bundle Line Bundle Normal Bundle Chern Class 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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