nLab
holonomic D-module

Contents

Idea

(Solutions of) holonomic systems of differential equations are formalized in the notion of a holonomic D-module. A D-module MM on a smooth complex analytic variety XX of dimension nn is holonomic if its characteristic variety is of dimension nn. It follows that the characteristic variety of a holonomic D-module is conic and lagrangian.

Holonomicity of D-modules is important also in geometric representation theory.

References

Lecture notes include

See also

  • Masaki Kashiwara, On the holonomic systems of linear differential equations. II, Invent. Math. 49 (1978), no. 2, 121–135, doi

  • Bernard Malgrange, On irregular holonomic D-modules, Séminaires et Congrès 8, 2004, p. 391–410, pdf; Équations différentielles à coefficients polynomiaux, Progress in Math. 96, Birkhäuser 1991. vi+232 pp.

  • P. Maisonobe, C. Sabbah, D-modules cohérents et holonomes, Hermann, Paris 1993.

  • V. Ginsburg, Characteristic varieties and vanishing cycles, Inv. Math. 84, 327–402 (1986)

Revised on February 16, 2014 08:12:18 by Urs Schreiber (89.204.155.248)