Deformation of Milnor Algebras
Abstract
We investigate deformations of Milnor algebras of smooth homogeneous polynomials, and prove in particular that any smooth degree d homogeneous polynomial in n+1 variables that is not of Sebastiani-Thom type is determined by the degree k homogeneous component of its Jacobian ideal for any d-1≤ k≤ (n+1)(d-2). Our results generalize the previous result on the reconstruction of a homogeneous polynomial from its Jacobian ideal.
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