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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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