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Degeneration of pole order spectral sequences for hyperplane arrangements of 4 variables
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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.
Forward citations
Cited by 2 Pith papers
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Solomon-Terao polynomials and Castelnouvo-Mumford regularity of hyperplane arrangements
For tame hyperplane arrangements, the Solomon-Terao polynomial is monic of degree equal to the number of hyperplanes, settling Conjecture 1.6.
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Addition theorems for Ziegler pairs of hyperplane arrangements
A new addition construction produces irreducible Ziegler pairs of hyperplane arrangements in arbitrary dimension, but the stated exponent formula in the main theorem is incorrect for dimensions at least five.
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