Vol. 305, No. 1, 2020
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Deformation of Milnor algebras

Zhenjian Wang
Vol. 305 (2020), No. 1, 329–338
DOI: 10.2140/pjm.2020.305.329
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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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