Symmetrizer group of a projective hypersurface

2025/01/15 by Jun-Muk Hwang, Hwang, Jun-Muk · 1 citation
Mathematics · #14J17 #14J70 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2501.08633

openalex publication_date 2025/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To each projective hypersurface which is not a cone, we associate an abelian linear algebraic group called the symmetrizer group of the corresponding symmetric form. This group describes the set of homogeneous polynomials with the same Jacobian ideal and gives a conceptual explanation of results by Ueda--Yoshinaga and Wang. In particular, the diagonalizable part of the symmetrizer group detects Sebastiani-Thom property of the hypersurface and its unipotent part is related to the singularity of the hypersurface.

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