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Riemann-Roch for Singular Varieties

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

Summary

The basic tool for a general Riemann-Roch theorem is MacPherson’s graph construction, applied to a complex E. of vector bundles on a scheme Y, exact off a closed subset X. This produces a localized Chern character1 \(ch_X^Y \left( {E.} \right)\) which lives in the bivariant group A (XY). For each class α ∈ A * Y, this gives a class
$$ch_X^Y \left( {E.} \right) \cap \alpha \in A_* X_\mathbb{Q} $$
whose image in A * Y is ∑(−1) i ch (E i ) ∩ α. The properties needed for Riemann-Roch, in particular the invariance under rational deformation, follow from the bivariant nature of \(ch_X^Y \left( {E.} \right)\).

Keywords

Vector Bundle Normal Bundle Coherent Sheaf Chern Character Singular Variety 
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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