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 k (n + 1)(d 2). 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