Complex Immersions and Arakelov Geometry

  • Jean-Michel Bismut
  • Henri Gillet
  • Christophe Soulé
Part of the Progress in Mathematics book series (MBC)


In this paper we establish an arithmetic Riemann-Roch-Grothendieck Theorem for immersions. Our final formula involves the Bott-Chern currents attached to certain holomorphic complexes of Hermitian vector bundles, which were previously introduced by the authors. The functorial properties of such currents are studied. Explicit formulas are given for Koszul complexes.


Exact Sequence Vector Bundle Normal Bundle Holomorphic Vector Bundle Smooth Section 
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Copyright information

© Springer Science+Business Media New York 2007

Authors and Affiliations

  • Jean-Michel Bismut
    • 1
  • Henri Gillet
    • 2
  • Christophe Soulé
    • 3
  1. 1.Dept. de Math. Bât 425Univ. de Paris-SudOrsayFrance
  2. 2.Dept. of Math.Univ. of IllinoisChicagoUSA
  3. 3.CNRS and IHESBures-sur-YvetteFrance

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