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Cones and Segre Classes

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

Summary

If X is a proper subvariety of a variety Y, the Segre class s (X, Y) of X in Y is the class in A * X defined as follows: let C = C X Y be the normal cone to X in Y, P(C) the projectivized normal cone, p the projection from P (C) to X. Then
$$s\left ( X,Y \right)=\sum_{i\leqq 0}P*\left (c_{1}\left ( O\left ( 1 \right) \right)^{i}\cap [P\left ( C \right)]\right)$$
.

Keywords

Vector Bundle Irreducible Component Local Ring Normal Cone Normal Bundle 
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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