论文标题
在非脱位超曲面的动机单构猜想周围
Around the motivic monodromy conjecture for non-degenerate hypersurfaces
论文作者
论文摘要
我们提供了一个新的几何证据，证明了尺寸为3 $的非脱位超曲面的动机单轨道猜想，这是由Lemahieu-van Proeyen and Bories-deys的工作证明的。更一般地，考虑到任何数量的变量中的非分级复杂多项式$ f $以及$ b_1 $ f $的$ b_1 $ facets $ f $的$ \ m m i \ m i \ mathbf {b} $，具有一致的基本方向，我们构建了一个堆栈堆栈嵌入$ f^{$ f^{0）$ f^{0）的堆叠式嵌入式构建的序列。 $ f $的动机zeta函数的原点仅来自$ \ mathbf {b} $中的方面。我们预计此处的结构可能会激发新的见解以及新的可能性，以解决猜想的解决方案。
We provide a new, geometric proof of the motivic monodromy conjecture for non-degenerate hypersurfaces in dimension $3$, which has been proven previously by the work of Lemahieu--Van Proeyen and Bories--Veys. More generally, given a non-degenerate complex polynomial $f$ in any number of variables and a set $\mathbf{B}$ of $B_1$-facets of the Newton polyhedron of $f$ with consistent base directions, we construct a stack-theoretic embedded desingularization of $f^{-1}(0)$ above the origin, whose set of numerical data excludes any known candidate pole of the motivic zeta function of $f$ at the origin that arises solely from facets in $\mathbf{B}$. We anticipate that the constructions herein might inspire new insights as well as new possibilities towards a solution of the conjecture.
