发表机构
Keio University; Institute of Mathematics, Vietnam Academy of Science and Technology（庆应义塾大学; 越南科学技术研究院数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造齐次多项式，其Milnor纤维达到Kato--Matsumoto连通性界且非形式，通过单纯多重楔与Suciu实现方法，回答了Suciu的两个问题。
AI 中文摘要
对于每个$n\geq 3$和$s\geq 2$，我们构造了一个次数为$n(n+1)/2$的齐次多项式，其Milnor纤维恰好是$2s$-连通的，并且其有理上同调在次数为$2s+1$的类上包含一个严格定义的非平凡$n$重Massey积，这意味着该Milnor纤维是非形式的，同时达到了Kato--Matsumoto连通性界。我们的构造基于Limonchenko引入的简单多胞形的神经复形的单纯多重楔，并结合了Suciu对加权齐次Milnor纤维的实现。由此，我们回答了Suciu提出的两个问题。
英文摘要
For every $n\geq 3$ and $s\geq 2$, we construct a homogeneous polynomial of degree $n(n+1)/2$ whose Milnor fiber is exactly $2s$-connected and whose rational cohomology contains a strictly defined nontrivial $n$-fold Massey product on classes of degree $2s+1$, implying that the Milnor fiber is non-formal, while attaining the Kato--Matsumoto connectivity bound. Our construction is based on the simplicial multiwedges of the nerve complexes of simple polytopes introduced by Limonchenko, combined with Suciu's realization of weighted homogeneous Milnor fibers. We thereby answer two problems posed by Suciu.
Comments16 pages, 1 figure
