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Nonisolated Saito singularities. (Russian) Zbl 0667.32010

With every hypersurface D in complex space one can associate an \({\mathcal O}_ m\)-module of tangent vector fields. If this module is locally free then D is a Saito’s divisor.
The author investigates the module \({\mathcal O}_ m\), the quality of subspace of singularities “sing D” of D. The main results are: “D is Saito’s divisor” and “sing D is a Cohen-Macaulay space” are equivalent, and the theory of local duality for isolated singularities is valid for nonisolated Saito’s singularities.
Reviewer: S.F.Krendelev

MSC:

32Sxx Complex singularities
32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
14J17 Singularities of surfaces or higher-dimensional varieties
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