关于Brieskorn格的结构，II
On the structure of Brieskorn lattices, II
摘要：
本文给出了形式Brieskorn格的好截面扩张的唯一性的一个简单证明，可用于C. Li，S. Li和K. Saito证明了非拟齐次多项式的收敛性。我们的证明使用了他们论文中的指数算子参数，尽管我们没有使用多向量场，也没有使用光滑的微分形式。我们还提出了一个明显更简单的算法，在Brieskorn-Pham多项式的情况下，原始形式的系数的归纳计算。在以前的一篇关于Brieskorn格结构的论文中，有一些观点还不是很清楚，我们对此给出了一些解释，例如，关于与良好部分相关的原始形式的存在性和唯一性，我们提出了一些有趣的例子。在附录中，我们证明了高阶剩余对在不同于主定理中的形式设置下的非零常数倍的唯一性。这是D. Shklyarov。
英文摘要：
We give a simple proof of the uniqueness of extensions of good sections for formal Brieskorn lattices, which can be used in a paper of C. Li, S. Li, and K. Saito for the proof of convergence in the non-quasihomogeneous polynomial case. Our proof uses an exponential operator argument as in their paper, although we do not use polyvector fields nor smooth differential forms. We also present an apparently simpler algorithm for an inductive calculation of the coefficients of primitive forms in the Brieskorn-Pham polynomial case. In a previous paper on the structure of Brieskorn lattices, there were some points which were not yet very clear, and we give some explanations about these, e.g. on the existence and the uniqueness of primitive forms associated with good sections, where we present some rather interesting examples. In Appendix we prove the uniqueness up to a nonzero constant multiple of the higher residue pairings in some formal setting which is different from the one in the main theorem. This is questioned by D. Shklyarov.
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