Bernstein polynomials and Milnor algebras

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RESUMO

Let f be an analytic germ on Cn+1. Then there is an analytic linear partial differential operator P with polynomial dependence on s, and a polynomial b(s), such that Pfs+1 = b(s)fs. This paper contains a simple existence proof and geometric interpretation in the case when f has an isolated critical zero at the origin, and is contained in its Jacobian ideal of first partial derivatives.

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