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Moduli of pre-\(\mathcal D\)-modules, perverse sheaves and the Riemann-Hilbert morphism. I. (English) Zbl 0853.14004
We construct a moduli scheme for semistable pre-\({\mathcal D}\)-modules with prescribed singularities and numerical data on a smooth projective variety. These pre-\({\mathcal D}\)-modules are to be viewed as regular holonomic \({\mathcal D}\)-modules with ‘level structure’. We also construct a moduli scheme for perverse sheaves on the variety with prescribed singularities and other numerical data, and represent the de Rham functor (which gives the Riemann-Hilbert correspondence) by an analytic morphism between the two moduli schemes.
Reviewer: N.Nitsure (Bombay)

MSC:
14D20 Algebraic moduli problems, moduli of vector bundles
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
32G81 Applications of deformations of analytic structures to the sciences
32C38 Sheaves of differential operators and their modules, \(D\)-modules
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