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Distinguished bases and Stokes regions for the simple and the simple elliptic singularities
Claus Hertling, Céline Roucairol
Isolated hypersurface singularities come equipped with a Milnor lattice, a -lattice of finite rank, and a set of -bases of this lattice. U…
Integral representations for solutions of exponential Gauss-Manin systems
Marco Hien, Celine Roucairol
Let f,g be two algebraically independent regular functions from the smooth affine complex variety U to the affine line. The associated exponential Gauss-Manin systems on the affine…
Formal structure of direct image of holonomic D-modules of exponential type
C. Roucairol
We compute formal invariants associated with the cohomology sheaves of the direct image of holonomic D-modules of exponential type. We also prove that every formal C[[t]]<\partial_…
Irregularity of an analogue of the Gauss-Manin systems
C. Roucairol
In the D-modules theory, Gauss-Manin systems are defined by the direct image of the structure sheaf O by a morphism. A major theorem says that these systems have only regular singu…