English

D-modules of pure Gaussian type and enhanced ind-sheaves

Algebraic Geometry 2022-12-26 v6 Complex Variables

Abstract

Differential systems of pure Gaussian type are examples of D-modules on the complex projective line with an irregular singularity at infinity, and as such are subject to the Stokes phenomenon. We employ the theory of enhanced ind-sheaves and the Riemann-Hilbert correspondence for holonomic D-modules of A. D'Agnolo and M. Kashiwara to describe the Stokes phenomenon topologically. Using this description, we perform a topological computation of the Fourier-Laplace transform of a D-module of pure Gaussian type in this framework, recovering and generalizing a result of C. Sabbah.

Keywords

Cite

@article{arxiv.2002.04327,
  title  = {D-modules of pure Gaussian type and enhanced ind-sheaves},
  author = {Andreas Hohl},
  journal= {arXiv preprint arXiv:2002.04327},
  year   = {2022}
}

Comments

28 pages, 4 figures; v6: final version, updated section numbering, added acknowledgements and publication details (manuscripta mathematica)