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Published online by Cambridge University Press: 29 May 2025
We discuss various aspects of the singularity invariants with differential origin derived from the D-module generated by ƒ s.
In this survey we discuss various aspects of the singularity invariants with differential origin derived from the D-module generated by ƒ s . We should like to point the reader to some other works: [Saito 2007] for V-filtration, Bernstein– Sato polynomials, multiplier ideals; [Budur 2012b] for all these and Milnor fibers; [Torrelli 2007] and [Narváez-Macarro 2008] for homogeneity and free divisors; [Suciu 2014] on details of arrangements, specifically their Milnor fibers, although less focused on D-modules.
Notation 1.1. In this article, X will denote a complex manifold. Unless indicated otherwise, X will be ℂn.
Throughout, let R = ℂ[x1, . . . , xn] be the ring of polynomials in n variables over the complex numbers. We denote by D = R (∂1, . . . , ∂n) the Weyl algebra. In particular, ∂i denotes the partial differentiation operator with respect to xi. If X is a general manifold, 𝒪X (the sheaf of regular functions) and 𝒪X (the sheaf of ℂ-linear differential operators on OX ) take the places of R and D.
If X = ℂn we use Roman letters to denote rings and modules; in the general case we use calligraphic letters to denote corresponding sheaves.
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