论文标题
牛顿非排级功能的附近周期公式的下降
Descent of nearby cycle formula for Newton non-degenerate functions
论文作者
论文摘要
我们证明了牛顿在原点及其动机版本的牛顿非分类函数的附近周期公式的下降定理（不假定便利条件）。这在某些论文中没有任何证据，尽管它的证明是不平凡的，这是由于坐标性超平面的存在，而这在有关下降定理的文献中被完全忽略了。在孤立的奇异案例中，它暗示了使用标准的权重标准估计值，这是Milnor Monodromy的Jordan块数量，具有最大值的Milnor单型块数量。它还提供了在隔离奇异案例中具有简单的牛顿多台面的非脱位函数的STEENBRINK猜想的修改版本的证明（在非震动情况下是错误的）。
We prove a descent theorem of nearby cycle formula for Newton non-degenerate functions at the origin as well as its motivic version (without assuming the convenience condition). This is used in some papers without any proof although its proof is quite nontrivial because of the existence of coordinate hyperplanes which is completely neglected in the literature about the descent theorem. In the isolated singularity case, it implies some well-known formula for the number of Jordan blocks of the Milnor monodromy with the theoretically maximal size, using a standard estimate of weights. It also provides a proof of a modified version of the Steenbrink conjecture on spectral pairs for non-degenerate functions with simplicial Newton polytopes in the isolated singularity case (which is false in the non-simplicial case).
