On Decomposition of D-modules and Bernstein-Sato polynomials for Hyperplane Arrangements
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Date
2016-06
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Addis Ababa University
Abstract
. This thesis discusses the relationship between Bernstein-Sato ideals of
= xy(a3x + y):::(amx + y); ai 2 C; ai 6= aj ;m _ 3
and the decomposition of the D2-module
M_ Chx; y; @x; @yi___
over the Weyl algebra Chx; y; @x; @yi, where for each i 2 f1; 2; :::;mg,
m ; _i 2 C
and _1 := x; _2 = y; _i := aix + y; (3 _ i _ m) are linear forms on C2. The thesis
starts by summarizing the de_nition, properties and the results on the number
of decomposition factors of M_
Then it continues with the de_nition and basic
properties of univariate Bernstein-Sato polynomials, and collects what is known of
Bernstein-Sato polynomials for hyperplane arrangements. A variation of the idea
are the multivariate Bernstein-Sato polynomials and ideals.
Main new results in the thesis are on the description of di_erent types of Bernstein-
Sato ideals of = xy
Qm
i=3(aix + y) (in chapter 4) and on the use of these ideals in
the decomposition of the D2-module M_
(in chapter
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On Decomposition of D-modules, and Bernstein-Sato