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

Abstract

For essential reduced hyperplane arrangements of 4 variables, we show that the pole order spectral sequence degenerates almost at $E_2$, and completely at $E_3$, generalizing the 3 variable case where the complete $E_2$-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.

7 pages

References in corpus (2)

• 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