关于Milnor-Orlik定理与可容许同时良好消解
On Milnor-Orlik's theorem and admissible simultaneous good resolutions
AI总结：
针对定义ℂ³原点孤立曲面奇点的可能牛顿退化加权齐次多项式及其通用形变族，证明存在可容许同时良好消解，并给出Milnor-Orlik定理弱版本的新几何证明。
摘要：
设$f$是（可能为牛顿退化的）加权齐次多项式，在$\u2102^3$原点处定义了一个孤立曲面奇点，设$\u200bf_s\u200b$是其系数的通用形变，满足当$s≠0$时$f_s$为牛顿非退化的。我们证明，对所有充分小的$s$（包括对应（可能牛顿退化的）函数$f$的$s=0$情形），函数族$f_s$存在“可容许的”同时良好消解。作为应用，我们给出了Milnor-Orlik定理一个弱版本的新几何证明，该定理断言$f$的单值化ζ函数（以及由此得到的其Milnor数）完全由其权、加权次数和牛顿边界决定。
英文摘要：
Let $f$ be a (possibly Newton degenerate) weighted homogeneous polynomial defining an isolated surface singularity at the origin of $\mathbb{C}^3$, and let $\{f_s\}$ be a generic deformation of its coefficients such that $f_s$ is Newton non-degenerate for $s\not=0$. We show that there exists an ''admissible'' simultaneous good resolution of the family of functions $f_s$ for all small $s$, including $s=0$ which corresponds to the (possibly Newton degenerate) function $f$. As an application, we give a new geometrical proof of a weak version of the Milnor-Orlik theorem that asserts that the monodromy zeta-function of $f$ (and hence its Milnor number) is completely determined by its weight, its weighted degree and its Newton boundary.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
