Bernstein-sato Polynomials of Arbitrary Varieties

We introduce the notion of Bernstein-Sato polynomial of an arbitrary variety, using the theory of V -filtrations of M. Kashiwara and B. Malgrange. We prove that the decreasing filtration of multiplier ideals coincides essentially with the restriction of the V -filtration. This implies a relation between the roots of the Bernstein-Sato polynomial and the jumping coefficients of the multiplier ideals, and also a relation between the maximal root of the polynomial and rational singularity in the case of a complete intersection. These are generalizations of the hypersurface case. We can calculate the polynomials explicitly in the case of monomial ideals.