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Vector Bundles and Chern Classes

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

Summary

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.

Keywords

Exact Sequence Vector Bundle Line Bundle Normal Bundle Chern Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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