Corpus ID: 235446629

Bernstein-Sato polynomials in commutative algebra

  title={Bernstein-Sato polynomials in commutative algebra},
  author={J. {\`A}. Montaner and Jack Jeffries and Luis N'unez-Betancourt},
This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra. 


Combinatorial Description of the Roots of the Bernstein–Sato Polynomials for Monomial Ideals
We give a combinatorial description of the roots of the Bernstein–Sato polynomial of a monomial ideal using the Newton polyhedron and some semigroups associated to the ideal.
On the computation of Bernstein-Sato ideals
This paper compares the approach of Briancon and Maisonobe for computing Bernstein–Sato ideals with the readily available method of Oaku and Takayama and shows that it can deal with interesting examples that have proved intractable so far. Expand
Zero loci of Bernstein–Sato ideals
We prove a conjecture of the first author relating the Bernstein-Sato ideal of a finite collection of multivariate polynomials with cohomology support loci of rank one complex local systems. ThisExpand
The asymptotics of integrals which depend on a critical point of a holomorphic function and the mixed Hodge structure in the vanishing cohomology are compared. Bibliography: 38 titles.
Bernstein-Sato Polynomials on Normal Toric Varieties
We generalize the Bernstein-Sato polynomials of Budur, Mustata and Saito to ideals in normal semigroup rings. In the case of monomial ideals, we also relate the roots of the Bernstein-Sato polynomialExpand
Roots of Bernstein-Sato polynomials for monomial ideals: a positive characteristic approach
We describe the roots of the Bernstein-Sato polynomial of a monomial ideal using reduction mod p and invariants of singularities in positive chracteristic. We give in this setting a positive answerExpand
On b-function, spectrum and multiplier ideals
We give a survey on b-function, spectrum, and multiplier ideals together with certain interesting relations among them including the case of arbitrary subvarieties.
Algorithm for Computing Bernstein-Sato Ideals Associated with a Polynomial Mapping
  • R. Bahloul
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • 2001
The aim is to present an algorithm for computing generators of Bjand B? of functional equations and related ideals called Bernstein?Sato ideals using standard basis techniques. Expand
Bernstein-Sato theory for arbitrary ideals in positive characteristic
Musta\c{t}\u{a} defined Bernstein-Sato polynomials in prime characteristic for principal ideals and proved that the roots of these polynomials are related to the $F$-jumping numbers of the ideal.Expand
Finiteness properties of local cohomology modules (an application ofD-modules to commutative algebra)
SummaryThe main goal of this paper is to establish finiteness properties of local cohomology modules in characteristic 0 that would be analogous to those proven by C. Huneke and R. Sharp inExpand