The Riemann-Roch theorem for algebraic manifolds

  • Friedrich Hirzebruch
Part of the Classics in Mathematics book series (volume 131)


In this chapter V is a complex n-dimensional manifold. The proof of the Riemann-Roch theorem depends on results on compact complex manifolds which are due to Cartan, Dolbeault, Kodaira, Serre and Spencer. These results are summarised in § 15. At two points in the proof it becomes necessary to make additional assumptions on V: first that V is a Kähler manifold (15.6–15.9) and then that V is algebraic.


Vector Bundle Line Bundle Cohomology Class CHERN Class Arithmetic Genus 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Friedrich Hirzebruch
    • 1
    • 2
  1. 1.Max-Planck-Institut für MathematikBonnGermany
  2. 2.Mathematisches InstitutUniversität BonnBonnWest Germany

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