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Abstract
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We investigate deformations of Milnor algebras of smooth homogeneous
polynomials, and prove in particular that any smooth degree
homogeneous
polynomial in
variables that is not of Sebastiani–Thom type is determined by the degree
homogeneous component of its Jacobian ideal for any
. 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
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Mathematical Subject Classification 2010
Primary: 14A25
Secondary: 14C34, 14J70
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Milestones
Received: 17 July 2019
Revised: 4 October 2019
Accepted: 4 October 2019
Published: 17 March 2020
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