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On the homological dimension of a Der-free hypersurface. (English) Zbl 0878.32012
Let \(\Omega\) be a germ of an analytic hypersurface at the origin of \({\mathbb{C}}^n\), \(D(\Omega)\) the left \({\mathcal O}_n\)-module of tangent holomorphic vector fields, \(R(\Omega)\) the algebra of holomorphic differential operators generated by \({\mathcal O}_n\) and \(D(\Omega)\). The hypersurface \(\Omega\) is said to be Der-free if \(D(\Omega)\) is a free \({\mathcal O}_n\)-module. In the case of Der-free \(\Omega\) the author calculates the homological dimension of \(R(\Omega)\).

MSC:
32C38 Sheaves of differential operators and their modules, \(D\)-modules
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