Introduction to a theory of b-functions

Abstract

We give an introduction to a theory of b-functions, i.e. Bernstein-Sato polynomials. After reviewing some facts from D-modules, we introduce b-functions including the one for arbitrary ideals of the structure sheaf. We explain the relation with singularities, multiplier ideals, etc., and calculate the b-functions of monomial ideals and also of hyperplane arrangements in certain cases.

arXiv comment15 pages, for the proceedings of a seminar at RIMS

References in corpus (2)

• A generalization of Griffiths' theorem on rational integrals
• Multiplier ideals, b-function, and spectrum of a hypersurface singularity

Cited by in corpus (1)

• On a theory of the $b$-function in positive characteristic