On Decomposition Of D-modules And Bernstein-sato Polynomials For Hyperplane Arrangements

. This thesis discusses the relationship between Bernstein-Sato ideals ofrn= xy(a3x + y):::(amx + y); ai 2 C; ai 6= aj ;m _ 3rnand the decomposition of the D2-modulernM_ Chx; y; @x; @yi___rnover the Weyl algebra Chx; y; @x; @yi, where for each i 2 f1; 2; :::;mg,rnm ; _i 2 Crnand _1 := x; _2 = y; _i := aix + y; (3 _ i _ m) are linear forms on C2. The thesisrnstarts by summarizing the de_nition, properties and the results on the numberrnof decomposition factors of M_rnThen it continues with the de_nition and basicrnproperties of univariate Bernstein-Sato polynomials, and collects what is known ofrnBernstein-Sato polynomials for hyperplane arrangements. A variation of the idearnare the multivariate Bernstein-Sato polynomials and ideals.rnMain new results in the thesis are on the description of di_erent types of Bernstein-rnSato ideals of = xyrnQmrni=3(aix + y) (in chapter 4) and on the use of these ideals inrnthe decomposition of the D2-module M_rn (in chapter

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