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

• Published in: Manuscripta mathematica Vol. 167; no. 3-4; pp. 435 - 467
• Main Author: Hohl, Andreas
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-03-2022; Springer Nature B.V
• Subjects: Algebraic Geometry; Calculus of Variations and Optimal Control; Optimization; Geometry; Laplace transforms; Lie Groups; Mathematics; Mathematics and Statistics; Modules; Number Theory; Sheaves; Topological Groups; 44A10; 34M40; 32C38
• ISSN: 0025-2611; 1432-1785
• DOI: 10.1007/s00229-021-01281-y

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 D’Agnolo and 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 Sabbah.