Deformation of Milnor Algebras

2019/06/12 by Zhenjian Wang, Wang, Zhenjian
Mathematics · #14A25 (Primary) #14C34 #14J70(Secondary) #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1906.04891

openalex publication_date 2019/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On homogeneous polynomials determined by their Jacobian ideal

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