论文标题
Bernstein-Sato理想和超平面布置
Bernstein-Sato ideals and hyperplane arrangements
论文作者
论文摘要
我们研究了伯恩斯坦 - 萨托理想的零基因座与B功能的根部之间的关系，并获得标准以确保可还原多项式的B-功能的根由相关的Bernstein-Sato Ideal的零基因座确定。应用标准以及Maisonobe的结果，我们证明了自由超平面布置的B功能的根集由其交点晶格确定。 我们还研究了伯恩斯坦 - 萨托理想的零基因座和任意中央超平面布置的相关相对特征周期。我们证明了Budur的多变量N/D猜想，以完全考虑任意超平面布置，这反过来又证明了相关的多变量拓扑Zeta函数的强烈单型猜想。
We study the relation between zero loci of Bernstein-Sato ideals and roots of b-functions and obtain a criterion to guarantee that roots of b-functions of a reducible polynomial are determined by the zero locus of the associated Bernstein-Sato ideal. Applying the criterion together with a result of Maisonobe we prove that the set of roots of the b-function of a free hyperplane arrangement is determined by its intersection lattice. We also study the zero loci of Bernstein-Sato ideals and the associated relative characteristic cycles for arbitrary central hyperplane arrangements. We prove the multivariable n/d conjecture of Budur for complete factorizations of arbitrary hyperplane arrangements, which in turn proves the strong monodromy conjecture for the associated multivariable topological zeta functions.
