Bernstein–Sato polynomials of arbitrary varieties
Bernstein–Sato polynomials of arbitrary varieties
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DOI：
10.1112/s0010437x06002193
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发表时间：
2004-08
影响因子：
1.8
通讯作者：
Nero Budur;M. Mustaţă;M. Saito
中科院分区：
文献类型：
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作者：
Nero Budur;M. Mustaţă;M. Saito
本文利用M的V-滤子理论，引入了任意簇（不一定是约化的，也不一定是不可约的）的Bernstein-Sato多项式的概念。Kashiwara和B。玛格兰奇我们证明了乘子理想的递减滤子与V-滤子的限制本质上是一致的。这意味着Bernstein-Sato多项式的根与乘子理想的跳跃系数之间的关系，以及在约化完全交的情况下多项式的最大根的有理奇点的判据。这些是超曲面情形的推广。我们可以在单项式理想的情况下显式地计算多项式。
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.