Bernstein-Sato polynomials for general ideals vs. principal ideals
Bernstein-Sato polynomials for general ideals vs. principal ideals
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一般理想与主理想的 Bernstein-Sato 多项式
DOI：
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发表时间：
2019
影响因子：
1
通讯作者：
M. Mustaţă
中科院分区：
文献类型：
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作者：
M. Mustaţă
证明了给定一个由光滑复变簇X上的正则函数f1，…，fr生成的理想I，I的Bernstein-Sato多项式等于函数g=sum_{i=1}，rf_iy_i在r维仿射空间的乘积上的简化Bernstein-Sato多项式.通过结合[BMS]的结果，我们将i的不变量和性质与g的不变量和性质联系起来。我们还利用Bernstein-Sato多项式的结果证明了主理想的Igusa Zeta函数的强单形猜想蕴含着对任意理想的类似的命题。
We show that given an ideal I generated by regular functions f_1,...,f_r on the smooth complex variety X, the Bernstein-Sato polynomial of I is equal to the reduced Bernstein-Sato polynomial of the function g=sum_{i=1}^rf_iy_i on the product of X with an r-dimensional affine space. By combining this with results from [BMS], we relate invariants and properties of I to those of g. We also use the result on Bernstein-Sato polynomials to show that the Strong Monodromy Conjecture for Igusa zeta functions of principal ideals implies a similar statement for arbitrary ideals.