Bernstein-Sato Polynomials in Commutative Algebra

DOI10.1007/978-3-030-89694-2_1zbMath1498.14042arXiv2106.08830OpenAlexW4212900249MaRDI QIDQ5051874

Luis Núñez-Betancourt, Josep Àlvarez Montaner, Jack Jeffries

Publication date: 18 November 2022

Published in: Commutative Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.08830

zbMATH Keywords

singularitiesmultiplier idealsBernstein-Sato polynomial\(D\)-module

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Singularities in algebraic geometry (14B05) Actions of groups on commutative rings; invariant theory (13A50) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Local cohomology and commutative rings (13D45) Commutative rings of differential operators and their modules (13N10) Rings of differential operators (associative algebraic aspects) (16S32) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35)

Related Items (1)

ON A BERNSTEIN–SATO POLYNOMIAL OF A MEROMORPHIC FUNCTION

Uses Software

• Macaulay2

Cites Work

• On certain rings of differentiable type and finiteness properties of local cohomology
• Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and Pfaffians
• Algorithms for checking rational roots of \(b\)-functions and their applications
• Bernstein-Sato polynomials for maximal minors and sub-maximal Pfaffians
• The Jacobian module, the Milnor fiber, and the \(D\)-module generated by \(f^s\)
• Yano's conjecture for two-Puiseux-pair irreducible plane curve singularities
• Some local consequences of Hodge theory
• Local systems on analytic germ complements
• Bernstein-Sato polynomials of hyperplane arrangements
• Bernstein-Sato ideals and local systems
• Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature
• Roots of Bernstein-Sato polynomials for monomial ideals: a positive characteristic approach
• \(D\)-modules generated by rational powers of holomorphic functions
• Discreteness and rationality of \(F\)-thresholds
• An introduction to homological algebra
• Local Bernstein-Sato ideals: algorithm and examples
• Racines de polynômes de Bernstein. (Zeros of Bernstein polynomials)
• On the structure of Brieskorn lattice
• Algorithme de calcul du polynome de Bernstein. Cas non dégéneré. (Algorithm of computation of Bernstein polynomials. The non-degenerate case)
• Micro-local analysis of prehomogeneous vector spaces
• An example of a ring Morita equivalent to the Weyl algebra \(A_ 1\).
• B-functions and holonomic systems. Rationality of roots of B-functions
• On the theory of b-functions
• Subellipticity of the \(\overline\partial\)-Neumann problem on pseudo- convex domains: sufficient conditions
• Bernstein polynomial and Tjurina number
• Differential operators on monomial rings
• Finiteness properties of local cohomology modules (an application of \(D\)- modules to commutative algebra)
• Bernstein-Sato's polynomial for several analytic functions
• An algorithm of computing \(b\)-functions
• Algorithms for the \(b\)-function and \(D\)-modules associated with a polynomial
• Algorithms for \(b\)-functions, restrictions, and algebraic local cohomology groups of \(D\)-modules
• \(D\)-modules, Bernstein-Sato polynomials and \(F\)-invariants of direct summands
• On a theory of the \(b\)-function in positive characteristic
• Invariant differential operators on the tangent space of some symmetric spaces
• The global homological dimension of the ring of differential operators on a nonsingular variety over a field of positive characteristic
• Polynôme de Bernstein générique. (Generic Bernstein polynomials)
• The analytic continuation of generalized functions with respect to a parameter
• Jumping coefficients of multiplier ideals
• Bernstein polynomials of a smooth function restricted to an isolated hypersurface singularity
• The \(D\)-module structure of \(F\)-split rings
• Generalized functional equations: transversality and principality of the Bernstein-Sato ideal
• Bernstein -- Sato polynomials on normal toric varieties
• Zero loci of Bernstein-Sato ideals
• Yano's conjecture
• Bigness of the tangent bundle of del Pezzo surfaces and \(D\)-simplicity
• Upper bounds for roots of \(b\)-functions, following Kashiwara and Lichtin
• Decompositions of Bernstein-Sato polynomials and slices
• Quantifying singularities with differential operators
• Cohomology support loci of local systems
• Magic matrix associated with a germ of plane curve and division by the Jacobian ideal
• Poles of the complex zeta function of a plane curve
• The \(V\)-filtration for tame unit \(F\)-crystals
• Bernstein-Sato polynomials in positive characteristic
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
• High order derivations. I
• Modules over a ring of differential operators. Study of the fundamental solutions of equations with constant coefficients
• Poles of \(| f(z,w)| ^{2s}\) and roots of the b-function
• On the computation of Bernstein-Sato ideals.
• Finiteness properties of local cohomology modules for regular local rings of mixed characteristic: the unramified case
• BERNSTEIN–SATO POLYNOMIALS AND TEST MODULES IN POSITIVE CHARACTERISTIC
• Principal intersection and bernstein-sato polynomial of an affine variety
• Algorithms for Bernstein--Sato polynomials and multiplier ideals
• Survey on the $D$-module $f^s$
• Test ideals in non-$\mathbb{Q}$-Gorenstein rings
• Cartier modules: Finiteness results
• An introduction to $p$-adic and motivic zeta functions and the monodromy conjecture
• On -modules related to the -function and Hamiltonian flow
• Theory of prehomogeneous vector spaces (algebraic part)—the English translation of Sato’s lecture from Shintani’s note
• Combinatorial Description of the Roots of the Bernstein–Sato Polynomials for Monomial Ideals
• Tight closure and strong F-regularity
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• On b-function, spectrum and multiplier ideals
• Singularities on normal varieties
• $F$-thresholds of hypersurfaces
• Rings of Differential Operators on Invariant Rings of Tori
• Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110)
• Fonctions D'Igusa p-adiques et Polynomes de Berstein
• Differential Operators on an Affine Curve
• La théorie du polynôme de Bernstein-Sato pour les algèbres de Tate et de Dwork-Monsky-Washnitzer
• Caracteristiques D'Euler-Poincare, Fonctions Zeta Locales et Modifications Analytiques
• Intégrales asymptotiques et monodromie
• Polynômes de Bernstein-Sato associés à une intersection complète quasi-homogène à singularité isolée
• On microlocal $b$-function
• F-Regularity, Test Elements, and Smooth Base Change
• Differential operators on Stanley-Reisner rings
• Singularities of Pairs
• On the ring of differential operators of certain regular domains
• On the existence of 𝐹-thresholds and related limits
• On theb-Functions of Hypergeometric Systems
• Localization, local cohomology, and the b-function of a D-module with respect to a polynomial
• Bernstein–Sato polynomial versus cohomology of the Milnor fiber for generic hyperplane arrangements
• Multiplier ideals, 𝑉-filtration, and spectrum
• A generalization of tight closure and multiplier ideals
• Lifting differential operators from orbit spaces
• Test ideals via algebras of 𝑝^{-𝑒}-linear maps
• Bernstein-Sato theory for arbitrary ideals in positive characteristic
• Bernstein–Sato functional equations, V-filtrations, and multiplier ideals of direct summands
• Bernstein-Sato polynomials for general ideals vs. principal ideals
• Combinatorially determined zeroes of Bernstein--Sato ideals for tame and free arrangements
• BERNSTEIN–SATO ROOTS FOR MONOMIAL IDEALS IN POSITIVE CHARACTERISTIC
• A remark on bigness of the tangent bundle of a smooth projective variety and D-simplicity of its section rings
• Bernstein–Sato polynomials of arbitrary varieties
• Resolution of Singularities and Division of Distributions
• Pseudo-differential operators in the theory of hyperfunctions
• Mixed Hodge modules
• Computations in algebraic geometry with Macaulay 2
• Polynômes de Bernstein associés à une fonction sur une intersection complète à singularité isolée. (Bernstein polynomials associated with a function on an isolated complete intersection singularity)
• Algorithm for computing Bernstein-Sato ideals associated with a polynomial mapping.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Bernstein-Sato Polynomials in Commutative Algebra