Degeneration of pole order spectral sequences for hyperplane arrangements of 4 variables

2019/02/11 by Morihiko Saito, Saito, Morihiko · 2 citations
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1902.03838

openalex publication_date 2019/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

For essential reduced hyperplane arrangements of 4 variables, we show that the pole order spectral sequence degenerates almost at E₂, and completely at E₃, generalizing the 3 variable case where the complete E₂-degeneration is known. These degenerations are useful to determine the roots of Bernstein-Sato polynomials supported at the origin. For the proof we improve an estimate of the Castelnuovo-Mumford regularity of logarithmic vector fields which was studied by H. Derksen and J. Sidman.

Citations

• Bernstein-Sato polynomials for projective hypersurfaces with weighted homogeneous isolated singularities
• Roots of Bernstein-Sato polynomials of certain homogeneous polynomials with two-dimensional singular loci

Cited by

• Addition theorems for Ziegler pairs of hyperplane arrangements
• Solomon-Terao polynomials and Castelnouvo-Mumford regularity of hyperplane arrangements

Related

• Roots of Bernstein-Sato polynomials of certain homogeneous polynomials with two-dimensional singular loci
• Bernstein-Sato polynomials for projective hypersurfaces with weighted homogeneous isolated singularities
• Multiplier ideals, b-function, and spectrum of a hypersurface singularity
• Spectrum of hyperplane arrangements in four variables
• Bernstein-Sato polynomials of hyperplane arrangements