Theory of (a, b)-Modules. I

  • Daniel Barlet
Part of the The University Series in Mathematics book series (USMA)


The aim of this chapter is to discuss a very simple algebraic structure that gives a systematic approach to a point of view that has appeared in Kyoji Saito [3] and Morihiko Saito [4, 5] in their study of isolated singularities of complex hypersurfaces. The idea is that the basic operation on asymptotic expansions at 0 with one variable (say s) is termwise integration (without constant). This operation is denoted by b. A second operation, denoted by a, is multiplication by s. The commutation relation ab — ba = b 2 shows that it is interesting to have a complete b-adic topology to work with. This leads us to a finiteness hypothesis over the ring ℂ[[b]] that is satisfied by the formal completion of the Brieskorn lattice of an isolated hypersurface singularity.


Induction Hypothesis Finite Type Simple Pole Bernstein Polynomial Formal Completion 
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    Morihiko Saito, Comment lire mon article “On the structure of Brieskorn lattice”, Notes manuscrites (~1984).Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Daniel Barlet
    • 1
  1. 1.Institut E. Cartan, UA 750 CNRSUniversité Nancy IVandoeuvreles-NancyFrance

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