Combinatorially determined zeroes of Bernstein--Sato ideals for tame and free arrangements
نویسندگان
چکیده
منابع مشابه
Local Bernstein-Sato ideals: Algorithm and examples
Let k be a field of characteristic 0. Given a polynomial mapping f = (f1, . . . , fp) from kn to kp, the local Bernstein–Sato ideal of f at a point a ∈ kn is defined as an ideal of the ring of polynomials in s = (s1, . . . , sp). We propose an algorithm for computing local Bernstein–Sato ideals by combining Gröbner bases in rings of differential operators with primary decomposition in a polynom...
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Using a generalization of Malgrange’s formula and a solution of Aomoto’s conjecture due to Esnault, Schechtman and Viehweg, we calculate the Bernstein-Sato polynomial (i.e. b-function) of a hyperplane arrangement with a reduced equation, and show that its roots are greater than−2 and the multiplicity of −1 coincides with the (effective) dimension. As a corollary we get a new proof of Walther’s ...
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Global and local Bernstein-Sato ideals, Bernstein-Sato polynomials and Bernstein-Sato polynomials of varieties are introduced, their basic properties are proven and their algorithmic determination with the method of Briançon/Maisonobe is presented. Strati cations with respect to the local variants of the introduced polynomials and ideals with the methods of Bahloul/Oaku and Levandovskyy/Martín-...
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Multiplier ideals are very important in higher dimensional geometry to study the singularities of ideal sheaves. It reflects the singularities of the ideal sheaves and provides strong vanishing theorem called the Kawamata-Viehweg-Nadel vanishing theorem (see [3]). However, the multiplier ideals are defined via a log resolution of the ideal sheaf and divisors on the resolved space, and it is dif...
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In this note we determine the Bernstein-Sato polynomial bQ(s) of a generic central arrangement Q = ∏k i=1 Hi of hyperplanes. We establish a connection between the roots of bQ(s) and the degrees of the generators for the top cohomology of the corresponding Milnor fiber. This connection holds for all homogeneous polynomials. We also introduce certain subschemes of the arrangement determined by th...
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ژورنال
عنوان ژورنال: Journal of Singularities
سال: 2020
ISSN: 1949-2006
DOI: 10.5427/jsing.2020.20h