发表机构
Capital Normal University（首都师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对全纯芽组建立迭代残差障碍，证明局部多变量拓扑ζ函数的极大阶极超平面及约化平面曲线芽组的实际极超平面均含于Bernstein–Sato零轨迹，从而证明平面曲线的拓扑多变量强单值群猜想。
AI 中文摘要
设$F=(f_1,\ldots,f_r)$是光滑复芽上的全纯芽组，$B_{F,0}$为其Bernstein–Sato理想。我们建立迭代残差障碍，证明SNC层上非零系数取值的残差类会迫使对应精确仿射参数落在$Z(B_{F,0})$中。作为应用，我们证明局部多变量拓扑ζ函数的所有极大阶极超平面均包含于Bernstein–Sato零轨迹，且对于约化平面曲线芽组对应的所有实际极超平面也成立；后者证明了平面曲线的拓扑多变量强单值群猜想。
英文摘要
We prove the multivariable Strong Monodromy Conjecture for the local topological zeta function of arbitrary tuples of nonzero nonunit plane curve germs. The entries may be nonreduced and may have common irreducible factors. We also prove that the non-equivariant local motivic and topological zeta functions have the same polar locus and generic pole orders, using a multivariable extension of the Nicaise--Xu definition of motivic pole order. Our arguments combine twisted Poincaré residues with resolution formulas and specialization to one variable. In arbitrary dimension, we prove that a nonzero iterated residue class on a stratum of a log resolution implies the vanishing of the Bernstein--Sato ideal at the corresponding parameter. In particular, every topological polar hyperplane whose order equals the ambient dimension is contained in this zero locus. For algebraic germs, the topological pole order is at most the motivic pole order, and the two attain maximal order simultaneously.
Commentsv3: 56 pages
