#### 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.

##### Keywords
Homogeneous polynomials, Milnor algebras, Macaulay inverse system
##### Mathematical Subject Classification 2010
Primary: 14A25
Secondary: 14C34, 14J70
##### Milestones
Received: 17 July 2019
Revised: 4 October 2019
Accepted: 4 October 2019
Published: 17 March 2020
##### Authors
 Zhenjian Wang Yau Mathematical Sciences Center Tsinghua University Beijing China