The Jacobian ideal of a hyperplane arrangement

2007/07/18 by Max Wakefield, Masahiko Yoshinaga, Wakefield, Max +1 · 1 citation
Computer Science · Mathematics · #32S22 (Secondary) #52C35 (Primary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0707.2672

openalex publication_date 2007/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Jacobian ideal of a hyperplane arrangement is an ideal in the polynomial ring whose generators are the partial derivatives of the arrangements defining polynomial. In this article, we prove that an arrangement can be reconstructed from its Jacobian ideal.

Cited by

• Bourbaki modules and the module of Jacobian derivations of projective hypersurfaces

Related

• On the Jacobian ideal of central arrangements
• New characterizations of freeness for hyperplane arrangements
• Localization of plus-one generated arrangements
• Geometric aspects of the Jacobian of a hyperplane arrangement
• Multiplier ideals of hyperplane arrangements