Homogeneous Polynomials with Isomorphic Milnor Algebras

TL;DR

This paper proves that two homogeneous polynomials with isomorphic Milnor algebras are right-equivalent, establishing a strong link between algebraic structure and polynomial equivalence.

Contribution

The paper demonstrates that isomorphic Milnor algebras imply right-equivalence for homogeneous polynomials, providing a new criterion for polynomial classification.

Findings

Isomorphic Milnor algebras imply right-equivalence for homogeneous polynomials

Establishes a correspondence between algebraic and geometric properties of polynomials

Advances understanding of polynomial classification via algebraic invariants

Abstract

In Theorem 3.2 we show that two homogeneous polynomials $f$ and $g$ having isomorphic Milnor algebras are right-equivalent.