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Moduli of Stokes torsors and singularities of differential equations. (English) Zbl 1508.14012

For a meromorphic connection \(\mathcal{M}\) with poles along a smooth divisor \(D\) in a smooth algebraic variety and with solution complex Sol \(\mathcal{M}\), the author proves that the good formal structure locus of \(\mathcal{M}\) coincides with the locus where the restrictions to \(D\) of Sol \(\mathcal{M}\) and Sol End \(\mathcal{M}\) are local systems. These loci are of very different natures.
The first one is defined via algebra, and the second via analysis. Nevertheless the proof of their coincidence is geometric. It is based on notions such as Stokes sheaves, Stokes loci, moduli of Stokes torsors, perverse sheaves, marked connections and on Mochizuki’s definition of good formal structure.

MSC:

14D22 Fine and coarse moduli spaces
34M40 Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain
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