On homogeneous polynomials determined by their Jacobian ideal
Zhenjian Wang
TL;DR
This paper explores which homogeneous polynomials can be uniquely identified by their Jacobian ideals, extending previous research and providing a comprehensive understanding of their determinacy.
Contribution
It extends and completes prior results on the determinacy of homogeneous polynomials by their Jacobian ideals, offering new insights into their characterization.
Findings
Characterization of polynomials determined by Jacobian ideals
Extension of previous results in polynomial determinacy
Complete classification in certain cases
Abstract
We investigate which homogeneous polynomials are determined by their Jacobian ideals, and extend and complete previous results due to J. Carlson and Ph. Griffiths, K. Ueda and M. Yoshinaga, and A. Dimca and E. Sernesi.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Algebraic Geometry and Number Theory · Advanced Combinatorial Mathematics