D-modules of pure Gaussian type and enhanced ind-sheaves
arXiv:2002.04327 · doi:10.1007/s00229-021-01281-y
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.
28 pages, 4 figures; v6: final version, updated section numbering, added acknowledgements and publication details (manuscripta mathematica)
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