Microfunction solutions of holonomic systems with irregular singularities

  • Naofumi Honda


One important feature of a holonomic system with regular singularities is that, if we consider the problem in the “complex holomorphic” category, its solution complex is cohomologically ℂ constructible. For example, for a pair of complex manifolds YX and a holonomic ε x module M with regular singularities, the solution complex
$$\hom {\varepsilon _x}(M,C_{Y|X}^{,f}$$
has ℂ constructible cohomologies where C Y|X f denotes the sheaf of tempered holomorphic microfunctions. However, for a holonomic module with irregular singularities, the solution complex (0.0) is no longer ℂ constructible in general. Such a breakdown of complex structure is deeply connected with Stokes lines of ordinary differential equations with irregular singularities. The purpose of this article is to investigate the relations between solutions of a system and the classical Stokes lines.


Infinite Order Stokes Line Growth Order Holonomic System Regular Singularity 
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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© Springer-Verlag Tokyo 1997

Authors and Affiliations

  • Naofumi Honda
    • 1
  1. 1.Department of Mathematics, Graduate School of ScienceHokkaido UniversitySapporo, Hokkaido 060Japan

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