Monge-Ampère Operators, Lelong Numbers and Intersection Theory

  • Jean-Pierre Demailly
Part of the The University Series in Mathematics book series (USMA)


This chapter is a survey article on the theory of Lelong numbers, viewed as a tool for studying intersection theory by complex differential geometry. We have not attempted to make an exhaustive compilation of the existing literature on the subject, nor to present a complete account of the state-of-the-art. Instead, we have tried to present a coherent unifying frame for the most basic results of the theory, based in part on our earlier works [7–10] and on Siu’s fundamental work [30]. To a large extent, the asserted results are given with complete proofs, many of them substantially shorter and simpler than their original counterparts. We only assume that the reader has some familiarity with differential calculus on complex manifolds and with the elementary facts concerning analytic sets and plurisubharmonic functions. The reader can consult Lelong’s books [25, 26] for an introduction to the subject. Most of our results still work on arbitrary complex analytic spaces, provided that suitable definitions are given for currents, plurisubharmonic functions, etc., in this more general situation. We have refrained ourselves from doing so for simplicity of exposition; we refer the reader to Ref. 9 for the technical definitions required in the context of analytic spaces.


Complex Manifold Comparison Theorem Plurisubharmonic Function Positive Current Finite Mass 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Jean-Pierre Demailly
    • 1
  1. 1.Institut FourierUniversité de Grenoble ISaint-Martin d’HèresFrance

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