Bernstein-Sato polynomials of arbitrary varieties

Details Bernstein-Sato polynomials of arbitrary varieties Bernstein-Sato polynomials of arbitrary varieties

2004-08-30

arxiv.org/abs/math/0408408v6

Mathematics

Algebraic Geometry

21 pages

Scientific paper

We introduce the notion of Bernstein-Sato polynomial of an arbitrary variety (which is not necessarily reduced nor irreducible), using the theory of V-filtrations of M. Kashiwara and B. Malgrange. We prove that the decreasing filtration by 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 criterion for rational singularities in terms of the maximal root of the polynomial in the case of a reduced complete intersection. These are generalizations of the hypersurface case. We can calculate the polynomials explicitly in the case of monomial ideals.

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