2006/05/01 by Nero Budur, Mircea Mustaţă, Morihiko Saito · 83 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic Geometry and Number Theory #Combinatorics #Complete intersection #Filtration (mathematics) #Gravitational singularity #Hypersurface #Mathematical analysis #Mathematics #Monomial #Multiplier (economics) #Nonlinear Waves and Solitons #Polynomial #Polynomial and algebraic computation #Pure mathematics #Variety (cybernetics)
paper · pdf · doi:10.1112/s0010437x06002193
published in Compositio Mathematica 142(03), 779-797 (Cambridge University Press)
openalex publication_date 2006/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We introduce the notion of the 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.