#### Vol. 305, No. 1, 2020

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Deformation of Milnor algebras

### Zhenjian Wang

Vol. 305 (2020), No. 1, 329–338
##### 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 $d-1\le k\le \left(n+1\right)\left(d-2\right)$. Our results generalize the previous result on the reconstruction of a homogeneous polynomial from its Jacobian ideal.

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