Bernstein–Sato polynomial versus cohomology of the Milnor fiber for generic hyperplane arrangements

DOI10.1112/S0010437X04001149zbMath1070.32021arXivmath/0204080MaRDI QIDQ4660025

Uli Walther

Publication date: 21 March 2005

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0204080

zbMATH Keywords

de Rham cohomologyhyperplane arrangementsMilnor fibersBernstein-Sato polynomiallogarithmic differential formsholonomic D-modulesrelative de Rham complexintegration functors

Mathematics Subject Classification ID

Relations with arrangements of hyperplanes (32S22) de Rham cohomology and algebraic geometry (14F40) Commutative rings of differential operators and their modules (13N10) Monodromy; relations with differential equations and (D)-modules (complex-analytic aspects) (32S40)

Related Items (21)

Bernstein-Sato Polynomials in Commutative Algebra ⋮ Local Cohomology—An Invitation ⋮ Generalized Lyubeznik numbers ⋮ \(D\)-modules, Bernstein-Sato polynomials and \(F\)-invariants of direct summands ⋮ Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and Pfaffians ⋮ Poles of the complex zeta function of a plane curve ⋮ A note on Bernstein-Sato varieties for tame divisors and arrangements ⋮ The monodromy conjecture for hyperplane arrangements ⋮ Algorithms for checking rational roots of \(b\)-functions and their applications ⋮ Combinatorially determined zeroes of Bernstein--Sato ideals for tame and free arrangements ⋮ Gröbner bases and logarithmic \(\mathcal D\)-modules. ⋮ Localization at hyperplane arrangements: combinatorics and \({\mathcal D}\)-modules ⋮ The Jacobian module, the Milnor fiber, and the \(D\)-module generated by \(f^s\) ⋮ Jumping coefficients and spectrum of a hyperplane arrangement ⋮ Decomposition of \(D\)-modules over a hyperplane arrangement in the plane ⋮ Bernstein-Sato polynomials of hyperplane arrangements ⋮ Linear free divisors and the global logarithmic comparison theorem ⋮ Decomposition factors of D-modules on hyperplane configurations in general position ⋮ Multiplier ideals of hyperplane arrangements ⋮ On Bernstein–Sato ideals for central line arrangements ⋮ Complements to Ample Divisors and Singularities

Uses Software

• Macaulay2
• Kan

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