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 $d-1\le k\le \left(n+1\right)\left(d-2\right)$. 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