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arXiv · 1902.03838

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

Morihiko Saito
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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.

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Morihiko Saito. 2019-02-11. Degeneration of pole order spectral sequences for hyperplane arrangements of 4 variables. https://arxiv.org/abs/1902.03838

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